Question

If $\alpha$ is non-real and $\alpha =\sqrt[5]{51},$ then the value of $2^{|1+\alpha +{\alpha }^2+{\alpha }^3-{\alpha }^{-1}-{\alpha }^{-2}|}$ is equal to

• A. 4
• B. 2
• C. 1
• D. none of these

Answer 1

The correct option is A 4

$\alpha =\sqrt[5]{51},$ $2^{|1+\alpha +{\alpha }^2+{\alpha }^3-{\alpha }^{-1}-{\alpha }^{-2}|}$

$\Rightarrow \alpha =1,$

$\Rightarrow 2^{|1+1+1+1-1-1|}=2^2=4.$

$2^{|1+\alpha +{\alpha }^2+{\alpha }^3-{\alpha }^{-1}-{\alpha }^{-2}|}=4$

Hence, the answer is $4.$