If $n^{2} + 5 = 5 (n + 1); n > 0$ , then find the cube of $n$ .

125

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1000

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1331

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0

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Solution

The correct option is A $125$
$n^{2} + 5 = 5 (n + 1)$
$\Rightarrow n^{2} + 5 = 5 n + 5$
$\Rightarrow n^{2} - 5 n = 0$
$\Rightarrow n (n - 5) = 0$
$\Rightarrow n = 0$ or $n = 5$
Since, $n > 0$
$∴ n^{3} = 5^{3} = 125$

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