if a + b + C is equal to 3 and a b + BC + CA is equal to 12 find a square + b square + c square
Answers
Answered by
3
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
Similar questions