Question

If x + $\frac{1}{x}$ = 2, then the value of $(x^2+\frac{1}{x^2})(x^3+\frac{1}{x^3})$ is

• A. $6$
• B. $4$
• C. $8$
• D. $16$

Answer 1

The correct option is B $4$

${(x+\frac{1}{x})}^2=4\Rightarrow .x^2+\frac{1}{x^2}=4-2=2$
${(x+\frac{1}{x})}^3=8$
$x^3+\frac{1}{x^3}+3(x+\frac{1}{x})=8$
$x^3+\frac{1}{x^3}=86=2$
Now $(x^2+\frac{1}{x^2})(x^3+\frac{1}{x^3})=2\times 2=4$