Mathematics: If $x$ and $y$ are positive real numbers for which $(x + y)^2 + (x - y)^2 = 10$ and $(x + y)^4 + (x - y)^4 = 98$, what is the value of $xy$? express your answer in simplest radical form.

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If $x$ and $y$ are positive real numbers for which

Ответ:

tristenmathews

14.01.2022

Mathematics

$\implies 2x^2+2y^2=10$
$\implies x^2+y^2=5$
$\implies (x^2+y^2)^2=x^4+2x^2y^2+y^4=25$

(x+y)^4+(x-y)^4=98

$\implies 2x^4+12x^2y^2+2y^4=98$
$\implies x^4+6x^2y^2+y^4=49$
$\implies 25+4x^2y^2=49$

4x^2y^2=24

$\implies x^2y^2=6$
$\implies xy=\sqrt6$

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Ответ:

Talber1

20.12.2020

Mathematics

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add the area

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If $x$ and $y$ are positive real numbers for which $(x + y)^2 + (x - y)^2 = 10$ and $(x + y)^4 + (x - y)^4 = 98$, what is the value of $xy$? express your answer in simplest radical form.

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