Question

If (a + b) = 16 and ab = 63 such that (a - b) > 0, then find the value of a² - b².
1. 23
2. 25
3. 52
4. 32

Answer 1

Correct Answer - Option 4 : 32

Given:

(a + b) = 16

ab = 63

Formula Used:

(a - b)² = (a + b)² - 4ab

Calculation:

We know that,

(a - b)2 = (a + b)2 - 4ab

⇒ (a - b)2 = (16)2 - 4 × 63

⇒ (a - b)2 = 256 - 252

⇒ (a - b)2 = 4

⇒ a - b = √4

⇒ a - b = 2

Now, a² - b² = (a + b)(a - b)

⇒ 16 × 2

⇒ 32

∴ The value of a2 - b2 is 32.