If $x - y = 4$ and $x y = 21$ then $x^{3} - y^{3} =$ ............

361

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316

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-188

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none of these

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Solution

The correct option is B 316
Given, $x - y = 4$ and $x y = 21$ ...(i)
$(x - y)^{2} = 4^{2}$
$\Rightarrow x^{2} + y^{2} - 2 x y = 16$
$\Rightarrow x^{2} + y^{2} - 2 \times 21 = 16$ (from (i))
$\Rightarrow x^{2} + y^{2} = 16 + 42 = 58$
Now, $x^{3} - y^{3} = (x - y) (x^{2} + y^{2} + x y)$
$= (4) (58 + 21) = 316$ (from(i))
Option B is correct.

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