If a - b = 4 and a^2 + b^2 = 40 where a and b are positive integers

• Quant Quadratic

If a - b = 4 and a² + b² = 40 where a and b are positive integers, where a and b are positive integers, then a³ + b⁶ is equal to

1. 264
2. 280
3. 300
4. 324

Answer

a - b = 4

Squaring both sides, 

(a - b)² = 16

a² + b² - 2ab = 16

40 - 2ab = 16

2ab = 24

Now, (a + b)² = a² + b² + 2ab = 40 + 24 = 64

a + b = 8

So, 2a = 12; a =6

and 2 b = 4; b = 2

Therefore, a³ + b⁶ = 6³ + 2⁶ = 216 + 64 = 280

The correct option is B.