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The Problem of Areas

If x+y=5 an...

Question

If $x + y = 5$ and $x^{2} + y^{2} = 111$ , then value of $x^{3} + y^{3}$ is:

770

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227

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555

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115

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Solution

The correct option is B $770$
Given, $x + y = 5, x^{2} + y^{2} = 111$
We know $x^{2} + y^{2} = (x + y)^{2} - 2 x y$
$\Rightarrow 111 = (5)^{2} - 2 x y \Rightarrow 2 x y = 25 - 111 = - 86 \Rightarrow x y = - 43$
Therefore, $x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})$
$= (5) (111 + 43) = 154 \times 5$
$= 770$

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