Question

If a² - b² = 88, a - b = 4 then find the value of ab.
1. 88
2. 2√26
3. 117
4. 22

Answer 1

Correct Answer - Option 3 : 117

Given:

a2 - b2 = 88

a - b = 4

Formula used:

a2 - b2 = (a - b)(a + b)

Calculation:

a - b = 4      ----(1)

(a - b)(a + b) = 88

⇒ 4 × (a + b) = 88

⇒ a + b = 88/4

⇒ a + b = 22      ----(2)

Adding equation (1) and equation (2), we get

⇒ a - b + a + b = 4 + 22

2a = 26

⇒ a = 13

Put the value of a in equation (2), we get

13 + b = 22

⇒ b = 9

value of ab = 13 × 9

⇒ ab = 117

∴ The value of ab is 117.