Question

plz answer as soon as possible

Answer 1

$given \: \: log_{y}x + log_{x}y = \frac{10}{3} \\ log_{y}x + \frac{1}{log_{y}x} = 3 + \frac{1}{3} \\ thus \: \: log_{y}x = 3 \\ so \: \: x = {y}^{3}$

$given \: \: xy = 144 \\ {y}^{3} \times y = 144 \\ {y}^{4} = 144 \\ y = \sqrt[4]{144} = 2 \sqrt{3} \\ therefore \: \: x = {(2 \sqrt{3}) }^{3} = 24 \sqrt{3}$

$thus \: \: \frac{x + y}{2 \sqrt{3} } = \frac{24 \sqrt{3} + 2 \sqrt{3} }{2 \sqrt{3} } = 13$