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Question
If `(28 - x)` is the mean proportional of `(23 - x)`and `(19 - x)` then find the value of x.
Solution
It is given that (28 − x) is the mean proportional of (23 − x) and (19 − x).
`therefore (23 − x)/(28- x) = (28 - x)/(19 - x)`
`therefore ( 28 - x )^2 = ( 23 - x) xx ( 19 - x )`
⇒ `(28)^2-2xx28x+x^2=437-23x-19x+x^2`
⇒ `784 - 56x + x^2 = 437 - 42x + x^2`
⇒ `784-437=-42x+x^2+56x-x^2`
⇒ `347 = 14x`
⇒ `x = 347/14`
Thus, the value of x is `347/14`.
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