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Identity (x+y)^2

If 2x2+2y2 ...

Question

If $2 x^{2} + 2 y^{2} = 640$ and $x + y = 18$ , what is the value of $x y$ ?

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Solution

The correct option is A $2$
$2 x^{2} + 2 y^{2} = 640$
$x^{2} + y^{2} = 320$ ...(i)
It is given that $(x + y) = 18$
Hence, $2 x y = (x + y)^{2} - (x^{2} + y^{2}) = 18^{2} - 320 = 324 - 320 = 4$
Hence, $2 x y = 4$ or $x y = 2$ .

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