Question

If $x+\frac{1}{x}=-2$, then the value of $x^7+\frac{1}{x^7}$ is

• A. $1$
• B. $-1$
• C. $0$
• D. $-2$

Answer 1

The correct option is D $-2$

$x+\left(\frac{1}{x}\right)=-2itwillbehappenonlywhenbothxand\left(\frac{1}{x}\right)areequal\therefore x+x=-2sox=-1then{x}^7+\left(\frac{1}{x^7}\right)=-1+\left(\frac{1}{(-7{)}^7}\right)=-2$