Question

If $x+\frac{1}{x}+2=0,$ then the value of $x^{33}+x^{32}+x^{13}+x^{12}+x+1$ is

• A. 0
• B. 1
• C. -1
• D. 2

Answer 1

The correct option is A 0

Given $x+2+\frac{1}{x}=0$

Multiply by $x$ both sides,

$x^2+2x+1=0$

$\Rightarrow (x+1{)}^2=0$

$\Rightarrow x+1=0$

$\Rightarrow x=-1$

The equation $x^{33}+x^{32}+x^{13}+x^{12}+x+1$

Put the value of $x=-1$

Then $(-1{)}^{33}+(-1{)}^{32}+(-1{)}^{13}+(-1{)}^{12}+(-1)+1=-1+1-1+1-1+1=3-3=0$