If $X + 3$ is the geometric mean between $X + 1$ and $X + 6,$ then find $X .$

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Solution

The correct option is C 3
Since $(X + 3)$ is the geometric mean between $(X + 1)$ and $(X + 6)$ , therefore,
$(X + 3)^{2} = (X + 1) (X + 6)$
$\Rightarrow X^{2} + 6 X + 9 = X^{2} + 7 X + 6$
$\Rightarrow 6 X + 9 = 7 X + 6$
$\Rightarrow 7 X - 6 X = 9 - 6$
$\Rightarrow X = 3$

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