Question

If a² + b² + c² = 74 and ab + bc + ca = 61, find the value of a + b + c.

Answer 1

Given: a² + b² + c² = 74 and ab + bc + ca = 61,

Using the identity,

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

(a + b + c)² = 74 + 2(61)

(a + b + c)² = 74 + 122

(a + b + c)² = 196

∴ a + b + c = `+-sqrt196`

∴ a + b + c = ±14