Question

If a² + b² + c² = 29 and ab + bc + ca = 26, find the value of a + b + c.

Answer 1

Given: a² + b² + c² = 29 and ab + bc + ca = 26,

Using the identity,

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

(a + b + c)² = 29 + 2(26)

(a + b + c)² = 29 + 52

(a + b + c)² = 81

∴ a + b + c = `+-sqrt81`

∴ a + b + c = ±9