Question

If x – y = 2 and x² + y² = 34, find the value of x³ – y³.

Answer 1

Given: x – y = 2 and x² + y² = 34

Step-wise calculation:

1. Start by finding (xy) using the identity:

(x – y)² = x² – 2xy + y²

Substitute the known values:

2² = 34 – 2xy 

4 = 34 – 2xy 

2xy = 34 – 4

2xy = 30

xy = 15

2. Use the identity for the difference of cubes:

x³ – y³ = (x – y)(x² + xy + y²)

We know:

x – y = 2

x² + y² = 34 

xy = 15

Calculate:

x² + xy + y² = 34 + 15

x² + xy + y² = 49

3. Substitute back into the difference of cubes formula:

x³ – y³ = 2 × 49

x³ – y³ = 98