Question

If a² + b² + c² = 38 and ab + bc + ca = 13, find the value of a + b + c.

Answer 1

Given: a² + b² + c² = 38 and ab + bc + ca = 13

Step-wise calculation:

1. Use the identity: 

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

2. Substitute the given values:

(a + b + c)² = 38 + 2 × 13

(a + b + c)² = 38 + 26

(a + b + c)² = 64

3. Take the square root of both sides:

a + b + c = ±8

Since the problem does not specify the sign, the value of a + b + c is either 8 or –8.