Question

Please Explain Answer of this question​

Answer 1

Answer:

hey here is your solution

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Step-by-step explanation:

$to \: find = \\ mean \: of \: a \: and \: b \\ \\ so \: here \\ \\ \frac{1}{a {}^{2} } - \frac{1}{b {}^{2} } = \frac{1}{c} \\ \\ ab = \sqrt{c} \: \: \: \: \: \: (1) \\ \\ thus \: then \\ \\ \frac{1}{a {}^{2} } - \frac{1}{b {}^{2} } = \frac{1}{c} \\ \\ \frac{b {}^{2} - a {}^{2} }{a {}^{2}b {}^{2} } = \frac{1}{c} \\ \\ = \frac{b {}^{2} - a {}^{2} }{(ab) {}^{2} } = \frac{1}{c} \\ \\ from \: (1) \\ we \: had \\ \\ \frac{b {}^{2} - a {}^{2} }{( \sqrt{c} ){}^{2} } = \frac{1}{c} \\ \\ = \frac{b {}^{2} - a {}^{2} }{c} = \frac{1}{c} \\ \\ b {}^{2} - a {}^{2} = 1 \\ \\ (b + a)(b - a) = 1 \\ \\ a + b = \frac{1}{b - a} \: \: \: \: \: \: \: (2)\\ \\ so \: thus \: then \\ \\ average \: (mean) \: of \: a \: and \: b = \frac{a + b}{2} \\ \\ from \: (2) \\ we \: had \\ \\ = \frac{ \frac{1}{b - a} }{2} \\ \\ = \frac{1}{2(b - a)}$