Question

if a + b + C is equal to 3 and a b + BC + CA is equal to 12 find a square + b square + c square

Answer 1

Given

a + b + c = 3

ab + bc + ca = 12

To Find

a² + b² + c²

Solution

First, we need to think of a formula that would have the application of the given variables. And that formula here is,

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

Substituting values we get,

⇒ (3)² = a² + b² + c² + 2ab + 2bc + 2ca

⇒ 9 = a² + b² + c² + 2[ab + bc + ca]

⇒ 9 = a² + b² + c² + 2[12]

⇒ 9 = a² + b² + c² + 24

⇒ - 24 + 9 = a² + b² + c²

⇒ - 15 = a² + b² + c²

a² + b² + c² = -15

Hence the value of a² + b² + c² is -15