Question

If a and b are two positive real numbers such that a + b = 20 and ab = 4, then the value of a³ + b³ is:
1. 7760
2. 240
3. 8000
4. 8240

Answer 1

Correct Answer - Option 1 : 7760

Given:

a and b are two positive real numbers such that a + b = 20 and ab = 4. We have to find the value of a³ + b³

Formula Used:

a3 + b³ = (a + b)³ – 3ab(a + b)

Calculation:

a3 + b3 = (a + b)3 – 3ab(a + b)

⇒ a3 + b³ = (20)³ – 3 × 4 × 20       [∵ Given a + b = 20 and ab = 4]

⇒ a3 + b³ = 20 × (20² – 12)

⇒ a3 + b³ = 20 × (400 – 12)

⇒ a3 + b³ = 20 × 388

⇒ a3 + b³ = 7760

∴ Value of a3 + b³ is 7760