Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (D)

4

Answer 2

If $a , b , c$ are in A.P. $\Rightarrow$ $2 b = a + c$

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

$= \frac { ( a - c ) ^ { 2 } 4 } { \left[ a ^ { 2 } + c ^ { 2 } + 2 a c - 4 a c \right] } = \frac { 4 ( a - c ) ^ { 2 } } { ( a - c ) ^ { 2 } } = 4$.

Trick : Put $a = 1 , b = 2 , c = 3$, then the required value is $\frac { 4 } { 1 } = 4$.