x-2-5-9-y-x-2-4-9-y-y-2-4-9-x-y-2-4-9-x-find-x-y-

Question Number 185122 by Shrinava last updated on 17/Jan/23

$$\begin{cases}{\sqrt{\mathrm{x}^{\mathrm{2}} \:−\:\frac{\mathrm{5}}{\mathrm{9}}\:+\:\sqrt{\mathrm{y}\:+\:\mathrm{x}^{\mathrm{2}} \:−\:\frac{\mathrm{4}}{\mathrm{9}}}}\:=\:\mathrm{y}}\\{\sqrt{\mathrm{y}^{\mathrm{2}} \:−\:\frac{\mathrm{4}}{\mathrm{9}}\:+\:\sqrt{\mathrm{x}\:+\:\mathrm{y}^{\mathrm{2}} \:−\:\frac{\mathrm{4}}{\mathrm{9}}}}\:=\:\mathrm{x}}\end{cases} \\ $$$$\mathrm{find}:\:\:\:\mathrm{x}\:,\:\mathrm{y}\:=\:? \\ $$

Commented by Frix last updated on 17/Jan/23

$$\mathrm{Is}\:\frac{\mathrm{5}}{\mathrm{9}}\:\mathrm{really}\:\mathrm{meant}\:\mathrm{or}\:\mathrm{is}\:\mathrm{it}\:\mathrm{a}\:\mathrm{typo}? \\ $$

Commented by Shrinava last updated on 17/Jan/23

$$\mathrm{sorry}\:\mathrm{yes}\:\mathrm{dear}\:\mathrm{ser}\:=\:\frac{\mathrm{5}}{\mathrm{9}} \\ $$

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