Is it easy?

Algebra Level 2

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

1 0 -1 2

1 solution

Asma Zugayar
Nov 9, 2015

Multiply both sides by x

x^2 +1 +2x =0

x^2+2x+1=0

(x+1)^2=0

=> x=-1

x to any even power equals 1

x to any odd power equals -1

x^33 +x^32+x^13+x^12+x+1

= -1+1 +-1+1+-1+1=0