Given positive even numbers $$ x,y $$ , if $$ x^2y+xy^2=96 $$ , find the value of $$ x^2+y^2 $$

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Uniteasy Admin · Accepted Answer

$$ x^2y+xy^2 $$
$$ =xy(x+y) $$
$$ =96 $$
$$ =2×2×24 $$
$$ =2×4×12 $$
$$ =4×4×6 $$
$$ =2×6×8 =2×6×(2+6) $$
$$ 	herefore x=2, y=6 $$
$$ x^2+y^2 $$
$$ =4+36 $$
$$ =40 $$

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