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Clever Algebraic Manipulations

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Positive real numbers $x,y$ satisfy the equations $x^2 + y^2 = 1$ and $x^4 + y^4= \frac{17}{18}$. Find $xy$.

ellapow Apr 1, 2021

Best Answer

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$(x^2+y^2)^2=1^2$

$x^4+y^4+2(xy)^2=1$

$\frac{17}{18}+2(xy)^2=1$

$xy=\sqrt{\frac{1}{36}}=\frac{1}{6}$

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Jamesaiden Apr 1, 2021

1⁺⁰ Answers

+150

+1

Best Answer

$(x^2+y^2)^2=1^2$

$x^4+y^4+2(xy)^2=1$

$\frac{17}{18}+2(xy)^2=1$

$xy=\sqrt{\frac{1}{36}}=\frac{1}{6}$

Jamesaiden Apr 1, 2021

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