Exams › SSC CGL (Prelims) › General

Given that $x+\frac{1}{x}=2$, determine the value of $x^8+\frac{1}{x^8}-2\left(x^6+\frac{1}{x^6}\right)+5\left(x^2+\frac{1}{x^2}\right).$

1. 4
2. 8
3. 10
4. 6

Correct answer: 8

Solution

From $x+\frac{1}{x}=2$, we get $(x-1)^2=0$, so $x=1$. Substituting into the expression gives $1+1-2(1+1)+5(1+1)=2-4+10=8$.

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