UGC NET CSE | December 2019 | Part 1 | Question: 18

Question

The sum of a number and its inverse is $-4$. The sum of their cubes is:

• A. $-52$
• B. $52$
• C. $64$
• D. $-64$

Answer 1

According to the question sum of number and it’s inverse is $-4$ that is :

$\bigg(x+\frac{1}{x}\bigg)=-4\dots\dots\dots(i)$

$\implies$ $\bigg( x+\frac{1}{x}\bigg)^3=(-4)^3$

$\because (a+b)^3=a^3+b^3+3ab(a+b)$

$\therefore \implies x^3+\frac{1}{x^3}+3*x*\frac{1}{x}(x+\frac{1}{x})=-64$

$\implies x^3+\frac{1}{x^3}+3(-4)=-64\dots\dot\dots\dots \text{from eq(i)}$

$\implies x^3+\frac{1}{x^3}=-64+12=-52$

Option $(A)$ is correct.