# Math Proof of the Week 1 Answer

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

Proof

Squaring $\frac{a +b}{a - b}$ results to

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

Now, since.

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

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

This means that

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

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

$\displaystyle\frac{a + b}{a - b}$

is positive.

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

## 3 thoughts on “Math Proof of the Week 1 Answer”

1. I’ll have to check my solution and see if it is longer or shorter or about the same.