Question

If x – y = 1 and xy = 2, then the value of x³ – y³ is ______.

Options

• 5

• 6

• 7

• 8

Answer 1

If x – y = 1 and xy = 2, then the value of x³ – y³ is 7.

Explanation:

Given:

• x – y = 1
• xy = 2

We need to find the value of x³ – y³.

Recall the identity: x³ – y³ = (x – y)(x² + xy + y²)

We already know x – y = 1 and xy = 2.

Next, find (x² + y²):

(x – y)² = x² – 2xy + y² 

1² = x² – 2(2) + y² 

1 = x² – 4 + y²

x² + y² = 5

Now, x² + xy + y² = (x² + y²) + xy

x² + xy + y² = 5 + 2

x² + xy + y² = 7

Therefore, x³ – y³ = (x – y)(x² + xy + y²)

x³ – y³ = 1 × 7

x³ – y³ = 7