If $x + y = 8; x y = 12$ then $x^{4} + y^{4}$ =_________

1012

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1112

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1212

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1312

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Solution

The correct option is D $1312$
$x + y = 8$
$S . O . B . S$
$(x + y)^{2} = 64$
$x^{2} + y^{2} + 2 x y = 64$
Given $x y = 12$
$x^{2} + y^{2} + 2 (12) = 64$
$x^{2} + y^{2} = 64 - 24$
$x^{2} + y^{2} = 40$
$S . O . B . S$
$(x^{2} + y^{2})^{2} = 40^{2}$
$x^{4} + y^{4} + 2 x^{2} y^{2} = 1600$
$x^{4} + y^{4} + 2 (12)^{2} = 1600$
$x^{4} + y^{4} = 1600 - 288$
$x^{4} + y^{4} = 1312$

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