Question

If ab + bc + ca = 31 and a² + b² + c² = 38, find the value of a + b + c.

Answer 1

Given: ab + bc + ca = 31 and a² + b² + c² = 38,

Using the identity,

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

(a + b + c)² = 38 + 2(31)

(a + b + c)² = 38 + 62

(a + b + c)² = 100

∴ a + b + c = `+-sqrt100`

∴ a + b + c = ±10