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}

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