Question

If x² + y² = 58 and xy = 21, find the value of x – y.

Answer 1

Given: x² + y² = 58 and xy = 21

Step-wise calculation:

1. Use the identity for the square of the difference of two numbers:

(x – y)² = x² + y² – 2xy

2. Substitute the given values:

(x – y)² = 58 – 2(21)

(x – y)² = 58 – 42

(x – y)² = 16

3. Taking the square root of both sides gives:

x – y = ±4

So the value of x – y is either 4 or –4.