Question

If $a , b , c$ are in G.P., then.

• A. $a \left( b ^ { 2 } + a ^ { 2 } \right) = c \left( b ^ { 2 } + c ^ { 2 } \right)$
• B. $a \left( b ^ { 2 } + c ^ { 2 } \right) = c \left( a ^ { 2 } + b ^ { 2 } \right)$
• C. $a ^ { 2 } ( b + c ) = c ^ { 2 } ( a + b )$
• D. None of these

Answer 1

Answer: (B)

$a \left( b ^ { 2 } + c ^ { 2 } \right) = c \left( a ^ { 2 } + b ^ { 2 } \right)$

Answer 2

If $a , b , c$ are in G.P. Then $b ^ { 2 } = a c$

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

$\Rightarrow$ $a \left( b ^ { 2 } + c ^ { 2 } \right) = c \left( a ^ { 2 } + b ^ { 2 } \right)$ .

Trick : Put $a = 1 , b = 2 , c = 4$ and check the alternates.