Question

3)If x + 5 is the mean proportion between x + 2 and x + 9, find the value of x​

Answer 1

ANSWER:

Given:

• x + 5 is mean proportion between x + 2 and x + 9.

To Find:

• Value of x.

Solution:

We are given that,

⟹ x + 5 is mean proportion between x + 2 and x + 9.

So, x + 2, x + 5 and x + 9 are in continued proportion.

⟹ (x + 2) : (x + 5) = (x + 5) : (x + 9)

⟹ (x + 2) / (x + 5) = (x + 5) / (x + 9)

On cross-multiplying,

⟹ (x + 5)(x + 5) = (x + 2)(x + 9)

⟹ (x + 5)^2 = (x + 2)(x + 9)

⟹ x^2 + 25 + 10x = x^2 + 2x + 9x + 18

⟹ x^2 + 25 + 10x = x^2 + 11x + 18

Cancelling x^2,

⟹ 25 - 18 = 11x - 10x

⟹ x = 7

Therefore, value of x = 7.

Verification:

⟹ (x + 2) : (x + 5) = (x + 5) : (x + 9)

Substituting value of x as 7,

⟹ (7 + 2) : (7 + 5) = (7 + 5) : (7 + 9)

⟹ (9) : (12) = (12) : (16)

Dividing LHS by 3 and RHS by 4,

⟹ 3 : 4 = 3 : 4

As, LHS = RHS.

HENCE VERIFIED!!!