Question

please answer guys urgent... please brainlist pucca​

Answer 1

Step-by-step explanation:

We have,

$\log \bigg( \frac{x + y}{3} \bigg) = \frac{1}{2}( \log(x) + \log(y))$

$\implies \log \bigg( \frac{x + y}{3} \bigg) = \frac{1}{2} \log(xy)$

$\implies \log \bigg( \frac{x + y}{3} \bigg) = \log( \sqrt{xy})$

$\implies \frac{x + y}{3} = \sqrt{xy}$

$\implies \bigg(\frac{x + y}{3} \bigg)^{2} = ( \sqrt{xy})^{2}$

$\implies \frac{x^{2} + y ^{2} + 2xy }{3} = xy$

$\implies x^{2} + y ^{2} + 2xy = 3xy$

$\implies x^{2} + y ^{2} = xy$

$\implies \frac{x^{2} + y ^{2}}{xy} = 1$

$\implies \frac{x^{2} }{xy} + \frac{ {y}^{2} }{xy} = 1$

$\implies \frac{x}{y} + \frac{y }{x} = 1$