Question

If a³ - b³ = 625, a² - b² = 25 and a + b = 5 then the value of a² + ab + b² is:
1. 125
2. 5
3. 25
4. 130

Answer 1

Correct Answer - Option 1 : 125

Given:

a3 - b3 = 625

a2 - b2 = 25

a + b = 5

Formulas used:

a2 - b2 = (a + b) (a - b)

a3 - b3 = (a - b) (a2 + ab + b2)

Calculation:

a2 - b2 = 25

⇒ (a + b)(a - b) = 25

⇒ 5(a - b) = 25

⇒ (a - b) = 5

a3 - b3 = 625

⇒ (a - b) (a2 + ab + b2) = 625

⇒ 5 × (a2 + ab + b2) = 625

⇒ (a2 + ab + b2) = 625/5 = 125

∴ The value of (a2 + ab + b2) is 125