Question

If x + y = 6 and xy = 8, find the value of x³ + y³.

Answer 1

Given: x + y = 6 and xy = 8

Step-wise calculation:

1. Use the identity for the sum of cubes:

x³ + y³ = (x + y)³ – 3xy(x + y)

2. Substitute the given values into the identity:

x³ + y³ = 6³ – 3 × 8 × 6 

x³ + y³ = 216 – 144

x³ + y³ = 72

So, the value of x³ + y³ is 72.