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Question Number 216911 by ArshadS last updated on 24/Feb/25

$$Findallpositiveinteger\mathrm{x},\mathrm{y}suchthat$$$${\mathrm{x}}^2+{\mathrm{y}}^2+\mathrm{xy}=169$$

Answered by A5T last updated on 25/Feb/25

$$\mathrm{WLOG},\mathrm{let}\mathrm{x}⩾\mathrm{y}$$$$\Rightarrow 169={\mathrm{x}}^2+{\mathrm{y}}^2+\mathrm{xy}⩾{3\mathrm{y}}^2\Rightarrow {\mathrm{y}}^2⩽\frac{169}{3}$$$$\Rightarrow \mathrm{y}⩽7$$$$\mathrm{Checking}\Rightarrow (\mathrm{x},\mathrm{y})=(8,7)$$

Commented by ArshadS last updated on 25/Feb/25

$$\mathrm{Nice}\mathrm{sir}!$$

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