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