Find : A2 + B2 + C2, If a + B + C = 9 and Ab + Bc + Ca = 24 - Mathematics

Sum

Find : a² + b² + c², if a + b + c = 9 and ab + bc + ca = 24

a+ b + c = 9

⇒ (a + b + c)² = (9)2

⇒ a² + b²+ c² + 2ab + 2bc + 2ca = 81

⇒ a²+ b² + c²+ 2(ab + bc + ca) = 81

⇒ a² + b² + c²+ 2×24 = 81

⇒ a² + b²+ c² + 48 = 81

⇒ a² + b²+ c²= 81 − 48

⇒ a² + b² + c² = 33

Concept: Application of Formulae

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Chapter 12: Identities - Exercise 12 (C) [Page 155]

Chapter 12 Identities
Exercise 12 (C) | Q 10 | Page 155

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