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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.
`\implies` (x + 2), (x + 5) and (x + 9) are in continued proportion.
`\implies` (x + 2) : (x + 5) = (x + 5) : (x + 9)
`\implies` (x + 5)2 = (x + 2)(x + 9)
`\implies` x2 + 25 + 10x = x2 + 2x + 9x + 18
`\implies` 25 – 18 = 11x – 10x
`\implies` x = 7
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