Question

solve this question.​

Answer 1

Step-by-step explanation:

$\sqrt{ \frac{x}{y} } + \sqrt{ \frac{y}{x} } = \frac{10}{3} \\ squiring \: both \: sides \: \\ ({ \sqrt{ \frac{x}{y} } + \sqrt{ \frac{y}{x} })}^{2} = ( { \frac{10}{3} })^{2} \\ \frac{x}{y} + \frac{y}{x} + 2 \times \sqrt{ \frac{x}{y} } \times \sqrt{ \frac{y}{x} } = \frac{100}{9} \\ \frac{x}{y} + \frac{y}{x} + 2 = \frac{100}{9} \\ \frac{ {x}^{2} + {y}^{2} }{xy} = \frac{100}{9} - 2 \\ \frac{ {x}^{2} + {y}^{2} }{xy} = \frac{100 - 18}{9} \\ \\ \frac{ {x}^{2} + {y}^{2} }{xy} = \frac{82}{9} \\ xy = \frac{9}{82} ( {x}^{2} + {y}^{2} )$

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