Question

If (28$-x$) is the mean proportional of (23$-x$) and (19$-x$) then find the vaue of x.

Answer 1

It is given that (28 − x) is the mean proportional of (23 − x) and (19 − x).

$$\begin{gathered} \therefore {\left(28-x\right)}^2=\left(23-x\right)\times \left(19-x\right) \\ \Rightarrow 784+x^2-56x=437-23x-19x+x^2 \\ \Rightarrow 784-56x=437-42x \\ \Rightarrow 56x-42x=784-437 \\ \Rightarrow 14x=347 \\ \Rightarrow x=\frac{347}{14} \end{gathered}$$
Thus, the value of x is $\frac{347}{14}$.