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Solid Geometry

If n 2 +4=1...

Question

If $n^{2} + 4 = 10 (n - 2)$ , then what is the cube of difference of $2$ roots ?

0

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Solution

The correct option is D $8$
$n^{2} + 4 = 10 (n - 2)$
$\Rightarrow n^{2} - 10 n + 24 = 0$
$\Rightarrow (n - 6) (n - 4) = 0$
$\Rightarrow n = 4, 6$
Difference $= 6 - 4 = 2$
Cube $2^{3}$ $= 8$

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