1-x-1-y-14-625-x-y-8-Find-all-solutions-

Question Number 208020 by Frix last updated on 02/Jun/24

{\begin{cases} \frac{1}{x} + \frac{1}{y} = \frac{14}{625} \\ \sqrt{x} + \sqrt{y} = 8 \end{cases}

Find all solutions .

Answered by efronzo1 last updated on 02/Jun/24

\Rightarrow x + y + 2 \sqrt{xy} = 64

\Rightarrow \frac{x + y}{xy} = \frac{14}{625}; x + y = \frac{14}{625} xy

\Rightarrow \frac{14}{625} {(\sqrt{xy})}^{2} + 2 \sqrt{xy} - 64 = 0

\Rightarrow (\sqrt{xy} - 25) (7 \sqrt{xy} + 800) = 0

\Rightarrow \sqrt{xy} = 25 or \underset{⏟}{ν}

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