SSC Selection Post 2020 PYQ — Question 71

The correct answer is Option 2 i.e. 180.

$x+\frac{1}{2x}={3}$

⇒ $2x+\frac{1}{x}={6}$

Cube both sides

⇒ $(2x+\frac{1}{x})^3={6}^3$

⇒ ${(2x)^3+(\frac{1}{x})^3+3\times(2x)({1\over x})(2x\times{1\over x})}=216$

⇒ $8x^3+\frac{1}{x^3}+6\times6=216$

⇒ $8x^3+\frac{1}{x^3}=216-36$

⇒ $8x^3+\frac{1}{x^3}=180$