Question

if√a+√b/√a-√b =9 then find a:b​

Answer 1

Answer:

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Step-by-step explanation:

$so \: here \: \\ \frac{ \sqrt{a} + \sqrt{b} }{ \sqrt{a} - \sqrt{b} } = 9 \\ so \: applying \: componendo \: dividendo \\ we \: get \\ \frac{ \sqrt{a} + \sqrt{b} + \sqrt{a } - \sqrt{b} }{ \sqrt{a} + \sqrt{b} - ( \sqrt{a} - \sqrt{b} ) } = \frac{9 + 1}{9 - 1} \\ \\ = \frac{ \sqrt{a} + \sqrt{a} }{ \sqrt{a} + \sqrt{b} - \sqrt{a} + \sqrt{b} } = \frac{10}{8} \: \\ \\ = \frac{ \sqrt{a} + \sqrt{a} }{ \sqrt{b} + \sqrt{b} } = \frac{10}{8}$

$= \frac{2 \sqrt{a} }{2 \sqrt{b} } = \frac{10}{8} \\ = \frac{ \sqrt{a} }{ \sqrt{b} } = \frac{10}{8} \\ squaring \: both \: sides \\ we \: get \\ \frac{ (\sqrt{a}) {}^{2} }{( \sqrt{b}) {}^{2} } = \frac{(10) {}^{2} }{(8) {}^{2} } \\ \\ = \frac{a}{b} = \frac{100}{64}$

$hence \: a : b = 100 : 64$