If a, b, c are in AP, then (a-c)2/(b2-ac) equals

Question: If $a,b,c$ are in AP, then $\dfrac{(a-c)^2}{b^2 - ac}$ equals

Answer: 4

Solution:

Given,

$= \dfrac{(a-c)^2}{b^2 - ac}$

$= \dfrac{(a+c)^2 - 4ac}{b^2 - ac}$

$= \dfrac{ (\frac{(a+c)^2}{4} - \frac{4ac}{4} )*4}{b^2 - ac}$

We know, $b = \frac{a+c}{2}$

$= \dfrac{b^2 - ac}{b^2 - ac} * 4$

$= 4$