If-a-x-b-y-a-x-b-y-1-then-a-x-b-y-

Question Number 208519 by Tawa11 last updated on 17/Jun/24

If a^{x} = b^{y}

\frac{a}{x} + \frac{b}{y} = 1

then, a^{x} + b^{y} = ?

Answered by mr W last updated on 17/Jun/24

a^{x} = b^{y} = k, s a y

x = \frac{\log k}{\log a}

y = \frac{\log k}{\log b}

\frac{a \log a}{\log k} + \frac{b \log b}{\log k} = 1

a \log a + b \log b = \log a^{a} b^{b} = \log k

\Rightarrow k = a^{a} b^{b}

a^{x} + b^{y} = 2 k = 2 a^{a} b^{b} ✓

Commented by Tawa11 last updated on 17/Jun/24

I appreciate sir .

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