If x + 5 is the mean proportional between x + 2 and x + 9; find the value of x.

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Solution

Given, x + 5 is the mean proportional between x + 2 and x + 9.
⟹ (x + 2), (x + 5) and (x + 9) are in continued proportion.
⟹ (x + 2) : (x + 5) = (x + 5) : (x + 9)
⟹ $(x + 5)^{2} = (x + 2) (x + 9)$
⟹ $x^{2} + 25 + 10 x = x^{2} + 2 x + 9 x + 18$
⟹25 − 18 = 11x − 10x
⟹ x = 7

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