# Find : a + B + C, If A2 + B2 + C2 = 83 and Ab + Bc + Ca = 71. - Mathematics

Sum

Find : a + b + c, if a2 + b2 + c2 = 83 and ab + bc + ca = 71.

#### Solution

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

⇒ (a + b + c)2 = 82 + 2(ab + bc + ca)

⇒ (a + b+ c)2 = 83 + 2×71

⇒ (a + b + c)2 = 83 + 142

⇒ (a + b + c)2 = 225

⇒ a + b + c = sqrt225

⇒ a + b +c = ±15

Concept: Application of Formulae
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#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 12 Identities
Exercise 12 (C) | Q 11 | Page 155