Question

The solution of the equation $= ( 1 + a ) \left( 1 + a ^ { 2 } \right) \left( 1 + a ^ { 4 } \right)$ is given by $x$ is equal to.

• A. 3
• B. 5
• C. 7
• D. None of these

Answer 1

Answer: (C)

7

Answer 2

We have

$\Rightarrow$ $\frac { \left( 1 - a ^ { x + 1 } \right) } { ( 1 - a ) } = ( 1 + a ) \left( 1 + a ^ { 2 } \right) + \left( 1 + a ^ { 4 } \right)$

$\Rightarrow$ $\left( 1 - a ^ { x + 1 } \right) = ( 1 - a ) ( 1 + a ) \left( 1 + a ^ { 2 } \right) \left( 1 + a ^ { 4 } \right)$

$\Rightarrow$ $\left( 1 - a ^ { x + 1 } \right) = \left( 1 - a ^ { 8 } \right)$ $\Rightarrow$ $x + 1 = 8$ $\Rightarrow$ $x = 7$.