If a/b+b/a = -1, a ≠ 0, b ≠ 0, then the value of 6(a³ - b³) is:

If a/b+b/a = -1, a ≠ 0, b ≠ 0, then the value of 6(a³…

If $\frac{a}{b}+\frac{b}{a}$ = -1, a ≠ 0, b ≠ 0, then the value of 6(a³ - b³) is:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 0

Given:

$\frac{a}{b}+\frac{b}{a}$ = -1

Formula Used:

a³ - b³ = (a - b)(a² + b² + ab)

Explanation:

According to the given question,

$\frac{a}{b}+\frac{b}{a}$ = -1 = a² + b²= -ab ⇒ a² + b² + ab = 0

Now, 6(a³ - b³ ) = 6(a - b)(a² + b² + ab) = 6(a - b) × 0 = 0

Hence the required answer is 0.