Question

If x + y = 10 and xy = 21, find the value of x² + y².

Answer 1

Given:

x + y = 10

xy = 21

Step-wise calculation:

Use the identity:

(x + y)² = x² + y² + 2xy

Rearranging:

x² + y² = (x + y)² – 2xy

Substitute the values:

x² + y² = 10² – 2 × 21

x² + y² = 100 – 42

x² + y² = 58

The value of x² + y² is 58.