Question

If x³ + y³ = 243 and x + y = 9, then find the value of xy.

1. 9
2. 18
3. 27
4. 36

Answer 1

Correct Answer - Option 2 : 18

Given:

x3 + y3 = 243

x + y = 9

Formula used:

(x + y)³ = x3 + y³ + 3xy(x + y)

Calculations:

x + y = 9

Cubing on both the sides,

(x + y)3 = 729

⇒ x3 + y3 + 3xy(x + y) = 729

⇒ 243 + 3xy × 9 = 729

⇒ 27xy = 486

⇒ xy = 18

∴ The value of xy is 18