Question

If $a,b$ and $c$ are in $A.P.,$ then $\frac{(a-c{)}^2}{b^2-ac}=$ ?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

$a,b,c$ are in A.P

So $2b=a+c$

Then

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

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

$\frac{a^2+c^2-2ac}{{\left(\frac{a+c}{2}\right)}^2-ac}=\frac{a^2+c^2-2ac}{\left(\frac{a^2+c^2-2ac}{2}\right)}=2$