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

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Sum

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

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Solution

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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APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 12 Identities
Exercise 12 (C) | Q 10 | Page 155
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