Question

If x + y = 6 and xy = 8, find the value of x² + y².

Answer 1

Given: x + y = 6 and xy = 8

Step-wise calculation:

Using the algebraic identity:

(x + y)² = x² + y² + 2xy

Substitute the given values:

6² = x² + y² + 2 × 8

36 = x² + y² + 16

Solve for x² + y²:

x² + y² = 36 – 16

x² + y² = 20

The value of x² + y² is 20.