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
Replies
12
Views
2K
POTW Integer n: Solving the Equation ##\dfrac{n^2+3}{2n+4}## for Integers
Replies
14
Views
1K
POTW Solve 3-Variable Equation with Real Solutions | √(z-y^2-6x-26)+x^2+6y+z-8=0
Replies
3
Views
1K
MHB How Can You Minimize This Complex Square Root Expression for Positive x and y?
Replies
6
Views
1K
POTW Prove that the roots of a polynomial cannot be all real
Replies
5
Views
1K
MHB Can x(x+y) Be Proved to Be ≤ 2 for Positive Real Numbers?
Replies
11
Views
2K
POTW Proving Inequality between Positive Real Numbers a and b: a(a+b) ≤ 2
Replies
6
Views
1K
MHB Maximize (x1+x2)(x1+x3)x4 for Quartic Equation with Real Roots in [1/2,2]
Replies
2
Views
1K
POTW Find Triplets of Positive Integers with Sum of Cubes
2
Replies
66
Views
3K
MHB Can You Verify This Trigonometric Identity Involving Cosecant Functions?
Replies
1
Views
1K
MHB What Is the Minimum Value of (a²+b²)/c² in Triangle ABC?
Replies
1
Views
1K
POTW Find the Sum of Two Real Numbers | Solve a + b with Given Equations
Replies
19
Views
2K
MHB Is the product of two radical expressions equal to six?
Replies
13
Views
1K
POTW Finding the Product of Real Roots: POTW Equation Solution
Replies
9
Views
1K
MHB What Is the Maximum Value of \( x \) in the Equation \( 2x+y+\frac{4}{xy}=10 \)?
Replies
7
Views
1K
MHB What Is the Minimum Cosine Value in Trigonometric Constraints?
Replies
2
Views
1K
MHB How Can We Find All Integer Pairs (k, n) That Satisfy This Factorial Equation?
Replies
4
Views
1K
MHB What is the minimum value of a+b+c+d if a^2-b^2+cd^2=2022?
Replies
5
Views
1K
MHB Minimum Value of (a+7)^2+(b+2)^2 with Constraint (a-5)^2+(b-7)^2=4 - POTW #506
Replies
5
Views
1K
MHB Minimum Sum of Non-Negative Integers with Given Equation - POTW #504
Replies
1
Views
1K
MHB Can $\sin^5 x + \cos^3 x$ Equal 1?
Replies
1
Views
1K
MHB Can This Infinite Product Surpass 50?
Replies
1
Views
999
MHB Can This Triangle Configuration Prove a Right Angle?
Replies
1
Views
1K
MHB Can You Prove the Polynomial Has Three Distinct Roots?
Replies
1
Views
1K
MHB Can $2^{\sqrt{12}}$ Exceed 11?
Replies
2
Views
1K
MHB What is the Range of $w(w+x)(w+y)(w+z)$ When $x+y+z+w=x^7+y^7+z^7+w^7=0$?
Replies
1
Views
1K
MHB Can Both Solutions of This Quadratic Equation Be Perfect Squares?
Replies
1
Views
1K
MHB How many positive integral solutions $(x,\,y)$ are there for the equation $\dfrac{1}{x+1}+\dfrac{1}{y}+\dfrac{1}{y(x+1)}=\dfrac{1}{2015}$?
Replies
1
Views
993
MHB What is the greatest 5-digit palindrome for 7n to be a 6-digit palindrome?
Replies
1
Views
1K
MHB How do you solve a system of equations with rational functions?
Replies
1
Views
1K
MHB Prove $0\le xy+yz+zx-2xyz\le7/27$ for $x+y+z=1$
Replies
1
Views
1K
MHB Can You Simplify This Trigonometric Expression?
Replies
1
Views
949
MHB How Does Solving P(x) Influence Q(x^2)?
Replies
1
Views
957
MHB Can You Prove This Inequality with Positive Real Numbers?
Replies
1
Views
1K
MHB How Do You Evaluate the Product of g(x) at the Roots of a Quintic Polynomial?
Replies
1
Views
965
MHB Sum of Cosine Values for $x$ | POTW #480 8/24/2021 | $100^{\circ}<x<200^{\circ}$
Replies
1
Views
1K
MHB What is the value of (x+y)(y+z)(z+x) if 1/(x+y+z) = 1/x + 1/y + 1/z?
Replies
1
Views
1K
MHB Find All Positive Integer Pairs for (x, y) in sqrt[3]{7x^2-13xy+7y^2}=|x-y|+1
Replies
1
Views
1K
MHB How to Evaluate the Expression for Roots of the Polynomial in POTW #476?
Replies
1
Views
1K
MHB What is the solution for evaluating $ab+cd$ with given constraints in POTW #477?
Replies
1
Views
952
MHB Can You Solve This Unique Fraction Challenge?
Replies
1
Views
1K
MHB Can you solve this week's POTW #474: Four real numbers with unique permutations?
Replies
1
Views
1K
MHB What Is the Largest Natural Number $n$ Such That $2^n$ Divides $3^{2016}-1$?
Replies
1
Views
1K
MHB Discover the Area of Points in a Unit Square | POTW #471
Replies
1
Views
940
MHB How Many Integer Solutions Exist for the Equation |x|+|y|+|z|=2010?
Replies
2
Views
986
MHB Prove Inequality: Integral of Square Root vs. Trigonometric Function
Replies
1
Views
1K
MHB Find Functions Satisfying $f^d(x)=2015-x$ for All Divisors of 2015
Replies
1
Views
967
MHB Can $(n^2+11n-4) \cdot n! + 33 \cdot 13^n + 4$ Be a Perfect Square?
Replies
2
Views
1K
MHB What is the Time Estimate for Completing a 1000-Piece Jigsaw Puzzle?
Replies
1
Views
1K
MHB Finding Extremes of x^3+y^3+z^3+xyz for Real Numbers with Constraints
Replies
1
Views
948
MHB Can You Solve This Week's Challenging System of Equations?
Replies
1
Views
1K
MHB Which Prime Numbers Make $2p^3 + 4p^2 - 3p + 12$ a Fifth Power?
Replies
1
Views
1K
MHB Is Every Positive Real Number a Solution to (x+1)(x+2)(x+5)≥36x?
Replies
1
Views
1K
MHB What Are the Possible Values of c for a Triangle with Area 5?
Replies
1
Views
942
MHB Can All Outputs of a Quadratic Function Be Integers?
Replies
1
Views
1K
MHB Can Non-zero Polynomials with Real Coefficients Have Real Roots in Common?
Replies
1
Views
1K
MHB Is it possible to find 6-digit numbers with a sum of 8?
Replies
1
Views
1K
MHB Possible Values: $f(8765)-f(4321)$ for Functions Satisfying Inequalities
Replies
1
Views
973
MHB How Do You Solve POTW #456 for (x+20)(y+20)(z+20)?
Replies
1
Views
994
MHB Can You Solve the Integer System xz-2yt=3 and xt+yz=1?
Replies
1
Views
1K
MHB What is the Greatest Value of an Expression with Given Numbers and Equation?
Replies
1
Views
1K
MHB Integer Solutions for Equation: POTW #453 - Feb 1st, 2021
Replies
1
Views
1K
MHB Can You Solve This Integer Equation for January 25th, 2021?
Replies
3
Views
1K
MHB How Many Divisors of $30^{2003}$ Are Not Divisors of $20^{2000}$?
Replies
1
Views
1K
MHB What are the solutions to x^3+3367=2^n?
Replies
1
Views
1K
MHB Triangle ABC: Find Possible Values of Cos A | POTW #449 Jan 4th 2021
Replies
2
Views
1K
MHB How to Tackle the Latest POTW Inequality Challenge?
Replies
2
Views
1K
MHB Can You Solve for a and b in This Trigonometric Equation?
Replies
1
Views
982
MHB Triangle with Complex Number Vertices SATISFIES Equilateral Relation
Replies
1
Views
1K
MHB Proof of Regular Heptagon Ratio: AD^3/AB^3 - (AB+2AC)/(AD-AC) = 1
Replies
1
Views
1K
MHB Maximum Value of Square Root Expression with Three Variables in [0,1]
Replies
2
Views
1K
MHB How Many Non-Congruent Triangles with Integer Sides Can a Given Perimeter Form?
Replies
1
Views
1K
MHB Is Sine of x Greater Than or Equal to 2x Over Pi for Angles Up to Pi/2?
Replies
1
Views
1K
MHB Can You Solve the Convex Quadrilateral Angle Mystery?
Replies
2
Views
1K
MHB Can All Roots of This Cubic Equation Be Bounded by 1?
Replies
1
Views
1K
MHB Is the Expression an Integer When Rational Conditions Apply?
Replies
1
Views
1K
MHB Can You Prove These Inequalities for Real Numbers a, b, and c?
Replies
2
Views
1K
MHB What are the solutions to a set of equations involving triple real numbers and specific conditions?
Replies
1
Views
1K
MHB Is It Possible to Prove Real Root Properties in Cubic Equations?
Replies
1
Views
1K
MHB What Is the Value of b If All Roots of the Polynomial Are Positive Real Numbers?
Replies
2
Views
1K
MHB Quadratic Polynomial Problem: Proving Equality with Real Numbers
Replies
1
Views
1K
MHB Solution to Problem #433: Proving a+b+c=0 yields 9
Replies
1
Views
1K
MHB How Many Final Points Can Be Reached in a Ten-Step Lattice Walk?
Replies
1
Views
1K
MHB How Do Divisors Relate in POTW #431's Integer Equation?
Replies
1
Views
1K
MHB Which Integers Make All Roots of This Polynomial Integer?
Replies
1
Views
1K
MHB How Do You Calculate the Sum of Sides and Diagonals of a Regular 12-Gon?
Replies
1
Views
1K
MHB How Can a Fifth Degree Polynomial Meet Specific Divisibility Conditions?
Replies
2
Views
1K
MHB Challenge: Find the Positive Integer for $133^5$ + $110^5$ + $84^5$ + $27^5$
Replies
1
Views
1K
MHB The value of $16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7$ is 1234.
Replies
1
Views
1K
MHB Can You Solve This Complex Radical Equation?
Replies
1
Views
1K
MHB Maximizing a in $ax^3+bx^2+cx+d$ with Constraints | POTW #424 07/06/2020
Replies
1
Views
1K
MHB How to Calculate the Sum of Squares in Complex Equation Systems?
Replies
1
Views
1K
MHB Problem #422: Four Non-Negative Real Numbers and a Unique Condition
Replies
1
Views
1K
MHB What Natural Numbers Solve the Equation from POTW #421?
Replies
1
Views
1K
MHB Find the Sum of Real Numbers Satisfying Equations
Replies
1
Views
1K
MHB What Is the Probability That a Bridge Is Empty at Noon?
Replies
1
Views
1K
MHB Can you solve this week's POTW: Integrating a Complex Expression? May 25th, 2020
Replies
1
Views
1K
MHB Acute Triangle ABC: Point P and Line Intersections Formula
Replies
1
Views
1K
MHB Can You Solve These Unique System of Equations?
Replies
1
Views
1K
MHB How Can One Non-Real Root Be Guaranteed in Equation #416?
Replies
1
Views
1K
You must log in or register to post here.

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.

Recent Insights

Back
Top