Math Proof of the Week 1 Answer

This is the proof to the first Math Proof Problem of the Week.

Proof 

Squaring $latex \frac{a +b}{a – b}$ results to

$latex \displaystyle \frac{a^2 + 2ab + b^2}{a^2-2ab + b^2}$

Now, since.

Since $latex a^2 + b^2 = 6$,

$latex \displaystyle \frac{a^2 + 2ab + b^2}{a^2-2ab + b^2} = \frac{6ab + 2ab}{6ab – 2ab} = \frac{8ab}{2ab} = 2$.

This means that

$latex \displaystyle \frac{a + b}{a – b} = \pm \sqrt{2}$

Now, since $latex a > b > 0$, $latex a – b$ is positive, which means that

$latex \displaystyle\frac{a + b}{a – b}$

is positive.

Therefore, $latex \frac{a + b}{a – b} = \sqrt{2}$

Math Proof Problem of the Week 1

It’s Friday and as I have mentioned in the previous post, I will be posting proof problems that are accessible to advanced high school students every Friday. Here is the Mathematics Proof Problem of the Week.

If $latex a > b > 0$, and $latex a^2 + b^2 = 6ab$, prove that

$latex \displaystyle\frac{a + b}{a – b} = \sqrt{2}$.

The proof of this problem and the second Math Proof of the Week will be posted next Friday.

Again, the problems in this series are intended for advanced high school math students. If the proof is too easy for you, no need to answer it. 🙂

New Series: Math Proof of the Week

I am starting a new series called Math Proof of the Week. This is very similar to Problem of the Week of the many websites on the internet. Each week, I will be giving a challenging mathematical proof problem which is accessible for high school students. The solutions of will be given the following week.

The problems will be given every Friday. This will give students weekend to cobble and solve the proof. The proof problems will involve the basic proofs in Algebra, Geometry, Number Theory, Elementary Calculus, Probability and Combinatorics. Of course, the problems are slightly more challenging than the ones I’m discussing in this blog.

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