NIELIT 2022 Feb Scientist C - Section D: 28

Question

When $2x + \frac{2}{x} = 3,$ then the value of $x^{3} + \frac{1}{x^{3}} + 2$ is :

• A. $7/2$
• B. $7/8$
• C. $8/7$
• D. $2/7$

Answer 1

Given that: $2x+\frac{2}{x}=3$

$\implies 2(x+1/x)=3$

$\implies (x+\frac{1}{x})=\frac{3}{2}…….(i)$

cubing eq (i) we get:

$\implies x^3+\frac{1}{x^3}+3*x*\frac{1}{x}(x+\frac{1}{x})=\frac{27}{8}$

$\implies x^3+\frac{1}{x^3}+3*\frac{3}{2}=\frac{27}{8}$

$\implies x^3+\frac{1}{x^3}=\frac{27}{8}-\frac{9}{2}$

Adding $+2$ in both side we get:

$\implies x^3+\frac{1}{x^3}+2 =\frac{27}{8}-\frac{9}{2}+2$

$\implies x^3+\frac{1}{x^3}+2=\frac{27-36+16}{8}=\frac{7}{8}$

Option (B) is correct.