Question

If ab + bc + ca = 27 and a² + b² + c² = 90, find the value of a + b + c.

Answer 1

Given: ab + bc + ca = 27 and a² + b² + c² = 90,

Using the identity,

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

(a + b + c)² = 90 + 2(27)

(a + b + c)² = 90 + 54

(a + b + c)² = 144

∴ a + b + c = `+-sqrt144`

∴ a + b + c = ±12