If-a-b-ab-find-the-value-of-a-b-a-b-

Question Number 216750 by sniper237 last updated on 17/Feb/25

I f a - b = \sqrt{a b} f i n d t h e v a l u e o f \frac{a - b}{a + b}

Answered by mr W last updated on 17/Feb/25

{(a + b)}^{2} = {(a - b)}^{2} + 4 a b = a b + 4 a b = 5 a b

\Rightarrow a + b = \pm \sqrt{5 a b}

\Rightarrow \frac{a - b}{a + b} = \pm \frac{\sqrt{a b}}{\sqrt{5 a b}} = \pm \frac{1}{\sqrt{5}} ✓

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