Question

please answer the question

$if \: \sqrt{x \div y} + \sqrt{y \div x} = 10 \div 3 \\ find \: the \: value \: of \: xy$
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Answer 1

Step-by-step explanation:

$\sqrt{} \frac{x}{y} + \sqrt{} \frac{y}{x} = \frac{10}{3} \\ let \: \sqrt{} \frac{x}{y} = a \\ a + \frac{1}{y} = \frac{10}{3} \\ \frac{a {2 + 1}^{} }{a} = \frac{10}{3} \\ {3}a {}^{2} + 3 = 10a \\ 3 {a}^{2} - 10a + 3 = 0 \\ 3 {a}^{2} - 9a - a + 3 = 0 \\ 3a(a - 3) - 1(y - 3) = 0 \\ (3a - 1)(y - 3) = 0 \\ \\ (3a - 1) = 0 \\ a = \frac{1}{3} \\ (a - 3) = 0 \\ a = 3$

a =√x/y

=>3=√x/y

=>9=x/y

=>x/9=y-----------(1)

a=1/3

x/y=1/9

=>9x=y

=>x=y/9----------(2)

xy=y/9×x/9

=xy/81

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