#### Question

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

#### 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 + 10x = x^{2} + 2x + 9x + 18

⇒ 25 – 18 = 11x – 10x

⇒ x = 7

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If X + 5 is the Mean Proportional Between X + 2 and X + 9; Find the Value of X. Concept: Proportions.

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