x-2-xy-y-2-7-x-3-y-2-xy-3-xy-2-Find-x-y-

Question Number 143584 by Huy last updated on 16/Jun/21

{\begin{cases} x^{2} - x y + y^{2} = 7 \\ (x + 3) (y - 2) = \sqrt{x y + 3} + \sqrt{x y - 2} \end{cases}

F i n d x, y

Answered by MJS_new last updated on 16/Jun/21

assuming both \sqrt{x y + 3} and \sqrt{x y - 2} are \in N

the only possibility is x y = 6 \Rightarrow y = \frac{6}{x}

inserting and transforming we get

{\begin{cases} x^{4} - 13 x^{2} + 36 = 0 \\ x^{2} + \frac{5 x}{2} - 9 = 0 \end{cases}

\Rightarrow x = 2 \Rightarrow y = 3

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