Số chính phương

T

tienqm123

$x^5 + y^5 = 2x^3y^3 $
\Rightarrow $\dfrac{x^2}{y^3}+ \dfrac{y^2}{x^3} = 2$
\Rightarrow $\dfrac{x^4}{y^6} + \dfrac{y^4}{x^6} + \dfrac{2}{xy} = 4 $
\Rightarrow $ \dfrac{x^4}{y^6} + \dfrac{y^4}{x^6} - \dfrac{2}{xy} = 4 - \dfrac{4}{xy}$
\Rightarrow $1-\dfrac{1}{xy} = (\dfrac{\dfrac{x^2}{y^3}-\dfrac{y^2}{x^3}}{2})^2$
\Rightarrow dpcm
 
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