Question

answer it..
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Answer 1

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

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

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

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

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

Squaring on both sides

$x^2+y^2+2xy = 9xy$

$x^2+y^2 = 7xy$

$\frac{x^2+y^2}{xy} = 7$

$\large\black\boxed{\frac{x}{y} + \frac{y}{x} = 7 }$