Question

if the mean proportional of (x-2) and (x-3) is x then find the valueof x

Answer 1

mean proportional mean square root of two number product.
this concept use here ,
root {(x-2)(x-3)}=x
squaring both side
(x-2)(x-3)=x^2
=> x^2-5x+6=x^2
=> -5x+6=0
=> x=6/5

Answer 2

$\bold{x=\frac{6}{5}}$  is the value of x if x is the mean proportion of $\bold{(x-2)(x-3).}$

Given:

$(x-2)(x-3)$

And x is the mean proportion  

To find:

The value of x

Solution:

Mean proportion is found by multiplying the given number  and taking the square roots of that answers gives the mean proportion.

Multiplying the given two number is $(x-2)(x-3)=x^{2}-3 x-2 x+6=x^{2}-5 x+6$

Given that the mean proportion of above 2 number is x.

Taking square on both sides  

$\begin{array}{l}{\sqrt{(x-2)(x-3)}=x} \\ {(x-2)(x-3)=x^{2}} \\ {x^{2}-5 x+6=x^{2}} \\ {-5 x+6=0}\end{array}$

$\begin{array}{l}{-5 x=-6} \\ {x=\frac{6}{5}}\end{array}$

Therefore, the value of $\bold{x=\frac{6}{5}}$ if the mean proportion of $\bold{(x-2)(x-3) is x.}}$