Question

If a + b + c = 7 and a² + b² + c² = 45, find the value of ab + bc + ca.

Answer 1

Given: a + b + c = 7 and a² + b² + c² = 45,

Using the identity,

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

(7)2 = 45 + 2(ab + bc + ca)

49 − 45 = 2(ab + bc + ca)

4 = 2(ab + bc + ca)

∴ ab + bc + ca = `4/2`

∴ ab + bc + ca = 2