Question

If a + b + c = 9 and ab + bc + ca = 14, find the value of a² + b² + c².

Answer 1

Given: a + b + c = 9 and ab + bc + ca = 14,

Using the identity,

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

(9)² = a² + b² + c² + 2(14)

81 = a² + b² + c² + 28

∴ a² + b² + c² = 81 − 28

∴ a² + b² + c² = 53