Question

If (a/b) + (b/a) = 1 then, find the value of a³ + b³.
1. 1
2. 2
3. 3
4. 0

Answer 1

Correct Answer - Option 4 : 0

Given:

(a/b) + (b/a) = 1

Formula used:

(a + b)² = a² + b² + 2ab

a³ + b³ = (a + b)(a2 + b² – ab)

Calculation:

(a/b) + (b/a) = 1

⇒ (a2 + b²)/(ab) = 1

⇒ (a2 + b2) = ab      ----(i)

a3 + b3 = (a + b)(a2 + b2 – ab)   

Putting the value of (a² + b²) from equation (i),

⇒ a3 + b3 = (a + b)(ab – ab)

⇒ 0

∴ The value of a3 + b³ is 0.