If \(\frac{a}{b} + \frac{b}{a} = -1\) and a - b = 2, then the value of a³ - b³is:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 3)

Answer 1

Given:

\(\frac{a}{b} + \frac{b}{a} = -1\)

Concept used:

if x + 1/x = - 1

then x³ = 1

Calculation:

Let (a/b) = x

Now the equation is:-

x + 1/x = - 1

So, x³ = 1------- (1)

Putting the value of x in eq.(1)

⇒ x3 = 1

⇒ (a/b)³ = 1

⇒ a³ = b³ ------- (2)

Putting the value of eq. (2) in the given equation:

⇒ a3 - b3

⇒ a3 - a3 = 0

∴ The correct answer is 0.

Alternate Method

Here, \(\frac{a}{b} + \frac{b}{a} = -1\)

⇒ \(\frac{a^2 + b^2}{ab} = -1\)

⇒ a2 + b2 + ab = 0

Now, a3 - b3 = (a - b) (a2 + ab + b2) = 2 × 0 = 0