MHB Minimum of $a$ for $a^2+2b^2+c^2+ab-bc-ac=1$

Thread starter anemone
Start date Apr 4, 2015
Tags

Minimum

Apr 4, 2015

anemone

Gold Member

MHB

POTW Director

Let $a,\,b,\,c$ be real numbers such that $a^2+2b^2+c^2+ab-bc-ac=1$. Find the minimum possible value of $a$.

Mathematics news on Phys.org

Apr 9, 2015

anemone

Gold Member

MHB

POTW Director

Hint:

Discriminant of quadratic equation helps...:)

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

View full post »

Thread 'Midpoint(s) of the unbounded number line'

Just chatting with my son about Maths and he casually mentioned that 0 would be the midpoint of the number line from -inf to +inf. I wondered whether it wouldn’t be more accurate to say there is no single midpoint. Couldn’t you make an argument that any real number is exactly halfway between -inf and +inf?

View full post »

Thread 'Arithmetic and our place value system'

A power has two parts. Base and Exponent. A number 423 in base 10 can be written in other bases as well: 1. 4* 10^2 + 2*10^1 + 3*10^0 = 423 2. 1*7^3 + 1*7^2 + 4*7^1 + 3*7^0 = 1143 3. 7*60^1 + 3*60^0 = 73 All three expressions are equal in quantity. But I have written the multiplier of powers to form numbers in different bases. Is this what place value system is in essence ?

View full post »

Similar threads

MHB Min Value of $\dfrac{a+3c}{a+2b+c}$+$\dfrac{4b}{a+b+2c}$+$\dfrac{8c}{a+b+3c}$

Nov 19, 2020

Replies: 1

Views: 2K

MHB Find length that minimizes the perimeter

Aug 6, 2020

Replies: 1

Views: 964

MHB The distance from AB = BC. AB = x^2 and BC = 9. Find AC.

Aug 12, 2017

Replies: 3

Views: 6K

Arithmetic mean and geometric mean

Oct 21, 2024

Replies: 1

Views: 2K

MHB Does Commutativity Hold for Matrices A and B with a Specific Matrix C?

Apr 28, 2022

Replies: 3

Views: 2K

I Are there any two pairs of integers with the same result in a specific function?

Jul 16, 2020

Replies: 7

Views: 2K

MHB Could you help me set up these geometric problems?

Jul 29, 2020

Replies: 2

Views: 3K

MHB Simplify a+b+c+d+2(ab+ac+ad+bc+bd+cd)+4(abc+abd+acd+bcd)+8(abcd)

Sep 20, 2019

Replies: 3

Views: 3K

MHB Therefore, AB + BC = AC, thus proving that the given equation is true.

Oct 27, 2017

Replies: 3

Views: 5K

MHB Solving for $(a,\,b,\,c)$ with Powers of 2

Apr 4, 2021

Replies: 1

Views: 1K

Bluesky LinkedIn

MHB Minimum of $a$ for $a^2+2b^2+c^2+ab-bc-ac=1$

Thread 'Trigonometry problem of interest'

Thread 'Midpoint(s) of the unbounded number line'

Thread 'Arithmetic and our place value system'

Similar threads

Hot Threads

Insights Fermat's Last Theorem

B What could prove this wrong? I'm having a dispute with friends

B About a definition: What is the number of terms of a polynomial P(x)?

B Geometry Puzzle with 20 points in a cross pattern

I Geometry problem of interest with a 3-4-5 triangle

Recent Insights

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Insights What Exactly is Dirac’s Delta Function? - Insight

Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight

Insights Fixing Things Which Can Go Wrong With Complex Numbers