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Question
Find two numbers such that the mean proportional between them is 14 and third proportional to them is 112.
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Solution
Let the required number be a and b.
Given, 14 is the mean proportional between a and b.
`=>` a : 14 = 14 : b
`=>` ab = 196
`=> a = 196/b` ...(1)
Also, given, third proportional to a and b is 112.
`=>` a : b = b : 112
`=>` b2 = 112a ...(2)
Using (1), we have
`b^2 = 112 xx 196/b`
b3 = (14)3(2)3
b = 28
From (1),
a = `196/28` = 7
Thus, the two numbers are 7 and 28.
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