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. Recall the identity:

(x + y)² = x² + y² + 2xy

2. Substitute the known values:

(x + y)² = 58 + 2 × 21

(x + y)² = 58 + 42

(x + y)² = 100

3. Take the square root on both sides:

`x + y = ±sqrt(100)`

x + y = ±10

Thus, the values of x + y are (+10) or (–10) depending on the signs of (x) and (y).