Math POTW for Secondary and High School Students Forum

POTW Inequality of Positive Real Numbers: Proving (1-1/x^2)(1-1/y^2)≥9 with x+y≤1
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POTW Integer n: Solving the Equation ##\dfrac{n^2+3}{2n+4}## for Integers
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14
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POTW Solve 3-Variable Equation with Real Solutions | √(z-y^2-6x-26)+x^2+6y+z-8=0
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3
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MHB How Can You Minimize This Complex Square Root Expression for Positive x and y?
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6
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POTW Prove that the roots of a polynomial cannot be all real
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5
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MHB Can x(x+y) Be Proved to Be ≤ 2 for Positive Real Numbers?
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11
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POTW Proving Inequality between Positive Real Numbers a and b: a(a+b) ≤ 2
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6
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MHB Maximize (x1+x2)(x1+x3)x4 for Quartic Equation with Real Roots in [1/2,2]
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2
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POTW Find Triplets of Positive Integers with Sum of Cubes
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66
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MHB Can You Verify This Trigonometric Identity Involving Cosecant Functions?
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1
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MHB What Is the Minimum Value of (a²+b²)/c² in Triangle ABC?
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1
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1K
POTW Find the Sum of Two Real Numbers | Solve a + b with Given Equations
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19
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MHB Is the product of two radical expressions equal to six?
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13
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POTW Finding the Product of Real Roots: POTW Equation Solution
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9
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MHB What Is the Maximum Value of \( x \) in the Equation \( 2x+y+\frac{4}{xy}=10 \)?
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7
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MHB What Is the Minimum Cosine Value in Trigonometric Constraints?
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2
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MHB How Can We Find All Integer Pairs (k, n) That Satisfy This Factorial Equation?
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4
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MHB What is the minimum value of a+b+c+d if a^2-b^2+cd^2=2022?
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5
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MHB Minimum Value of (a+7)^2+(b+2)^2 with Constraint (a-5)^2+(b-7)^2=4 - POTW #506
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5
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1K
MHB Minimum Sum of Non-Negative Integers with Given Equation - POTW #504
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1
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976
MHB Can $\sin^5 x + \cos^3 x$ Equal 1?
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1
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1K
MHB Can This Infinite Product Surpass 50?
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1
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955
MHB Can This Triangle Configuration Prove a Right Angle?
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1
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MHB Can You Prove the Polynomial Has Three Distinct Roots?
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1
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966
MHB Can $2^{\sqrt{12}}$ Exceed 11?
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2
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MHB What is the Range of $w(w+x)(w+y)(w+z)$ When $x+y+z+w=x^7+y^7+z^7+w^7=0$?
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1
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989
MHB Can Both Solutions of This Quadratic Equation Be Perfect Squares?
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1
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MHB How many positive integral solutions $(x,\,y)$ are there for the equation $\dfrac{1}{x+1}+\dfrac{1}{y}+\dfrac{1}{y(x+1)}=\dfrac{1}{2015}$?
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1
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952
MHB What is the greatest 5-digit palindrome for 7n to be a 6-digit palindrome?
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1
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MHB How do you solve a system of equations with rational functions?
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1
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MHB Prove $0\le xy+yz+zx-2xyz\le7/27$ for $x+y+z=1$
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1
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979
MHB Can You Simplify This Trigonometric Expression?
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1
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906
MHB How Does Solving P(x) Influence Q(x^2)?
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1
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914
MHB Can You Prove This Inequality with Positive Real Numbers?
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1
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MHB How Do You Evaluate the Product of g(x) at the Roots of a Quintic Polynomial?
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1
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925
MHB Sum of Cosine Values for $x$ | POTW #480 8/24/2021 | $100^{\circ}<x<200^{\circ}$
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1
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MHB What is the value of (x+y)(y+z)(z+x) if 1/(x+y+z) = 1/x + 1/y + 1/z?
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1
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1K
MHB Find All Positive Integer Pairs for (x, y) in sqrt[3]{7x^2-13xy+7y^2}=|x-y|+1
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1
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MHB How to Evaluate the Expression for Roots of the Polynomial in POTW #476?
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1
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982
MHB What is the solution for evaluating $ab+cd$ with given constraints in POTW #477?
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1
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913
MHB Can You Solve This Unique Fraction Challenge?
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1
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978
MHB Can you solve this week's POTW #474: Four real numbers with unique permutations?
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1
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MHB What Is the Largest Natural Number $n$ Such That $2^n$ Divides $3^{2016}-1$?
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1
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MHB Discover the Area of Points in a Unit Square | POTW #471
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1
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MHB How Many Integer Solutions Exist for the Equation |x|+|y|+|z|=2010?
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2
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MHB Prove Inequality: Integral of Square Root vs. Trigonometric Function
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1
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MHB Find Functions Satisfying $f^d(x)=2015-x$ for All Divisors of 2015
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1
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924
MHB Can $(n^2+11n-4) \cdot n! + 33 \cdot 13^n + 4$ Be a Perfect Square?
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2
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959
MHB What is the Time Estimate for Completing a 1000-Piece Jigsaw Puzzle?
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1
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MHB Finding Extremes of x^3+y^3+z^3+xyz for Real Numbers with Constraints
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1
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907
MHB Can You Solve This Week's Challenging System of Equations?
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1
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MHB Which Prime Numbers Make $2p^3 + 4p^2 - 3p + 12$ a Fifth Power?
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1
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MHB Is Every Positive Real Number a Solution to (x+1)(x+2)(x+5)≥36x?
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1
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MHB What Are the Possible Values of c for a Triangle with Area 5?
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1
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902
MHB Can All Outputs of a Quadratic Function Be Integers?
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1
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MHB Can Non-zero Polynomials with Real Coefficients Have Real Roots in Common?
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1
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MHB Is it possible to find 6-digit numbers with a sum of 8?
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1
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MHB Possible Values: $f(8765)-f(4321)$ for Functions Satisfying Inequalities
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1
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929
MHB How Do You Solve POTW #456 for (x+20)(y+20)(z+20)?
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1
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950
MHB Can You Solve the Integer System xz-2yt=3 and xt+yz=1?
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1
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MHB What is the Greatest Value of an Expression with Given Numbers and Equation?
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1
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MHB Integer Solutions for Equation: POTW #453 - Feb 1st, 2021
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1
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MHB Can You Solve This Integer Equation for January 25th, 2021?
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3
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MHB How Many Divisors of $30^{2003}$ Are Not Divisors of $20^{2000}$?
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1
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MHB What are the solutions to x^3+3367=2^n?
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1
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MHB Triangle ABC: Find Possible Values of Cos A | POTW #449 Jan 4th 2021
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2
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MHB How to Tackle the Latest POTW Inequality Challenge?
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2
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MHB Can You Solve for a and b in This Trigonometric Equation?
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1
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MHB Triangle with Complex Number Vertices SATISFIES Equilateral Relation
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1
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MHB Proof of Regular Heptagon Ratio: AD^3/AB^3 - (AB+2AC)/(AD-AC) = 1
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1
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998
MHB Maximum Value of Square Root Expression with Three Variables in [0,1]
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2
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MHB How Many Non-Congruent Triangles with Integer Sides Can a Given Perimeter Form?
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1
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MHB Is Sine of x Greater Than or Equal to 2x Over Pi for Angles Up to Pi/2?
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1
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MHB Can You Solve the Convex Quadrilateral Angle Mystery?
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2
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MHB Can All Roots of This Cubic Equation Be Bounded by 1?
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1
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MHB Is the Expression an Integer When Rational Conditions Apply?
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1
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963
MHB Can You Prove These Inequalities for Real Numbers a, b, and c?
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2
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MHB What are the solutions to a set of equations involving triple real numbers and specific conditions?
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1
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MHB Is It Possible to Prove Real Root Properties in Cubic Equations?
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1
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MHB What Is the Value of b If All Roots of the Polynomial Are Positive Real Numbers?
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2
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MHB Quadratic Polynomial Problem: Proving Equality with Real Numbers
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1
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MHB Solution to Problem #433: Proving a+b+c=0 yields 9
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1
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995
MHB How Many Final Points Can Be Reached in a Ten-Step Lattice Walk?
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1
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MHB How Do Divisors Relate in POTW #431's Integer Equation?
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1
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MHB Which Integers Make All Roots of This Polynomial Integer?
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1
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MHB How Do You Calculate the Sum of Sides and Diagonals of a Regular 12-Gon?
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1
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MHB How Can a Fifth Degree Polynomial Meet Specific Divisibility Conditions?
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2
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MHB Challenge: Find the Positive Integer for $133^5$ + $110^5$ + $84^5$ + $27^5$
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1
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MHB The value of $16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7$ is 1234.
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1
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MHB Can You Solve This Complex Radical Equation?
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1
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MHB Maximizing a in $ax^3+bx^2+cx+d$ with Constraints | POTW #424 07/06/2020
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1
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MHB How to Calculate the Sum of Squares in Complex Equation Systems?
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1
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MHB Problem #422: Four Non-Negative Real Numbers and a Unique Condition
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1
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MHB What Natural Numbers Solve the Equation from POTW #421?
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1
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MHB Find the Sum of Real Numbers Satisfying Equations
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1
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1K
MHB What Is the Probability That a Bridge Is Empty at Noon?
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1
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MHB Can you solve this week's POTW: Integrating a Complex Expression? May 25th, 2020
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1
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MHB Acute Triangle ABC: Point P and Line Intersections Formula
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1
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MHB Can You Solve These Unique System of Equations?
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1
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MHB How Can One Non-Real Root Be Guaranteed in Equation #416?
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1
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POTW High School

Welcome to the High School POTW forum!

Math problems will be posted each week on Monday, most likely early in the morning (1am, 2am, etc.) Eastern Standard Time. There will be one math problem each week at the advanced high school student or secondary level.

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