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Question
Find : a + b + c, if a2 + b2 + c2 = 83 and ab + bc + ca = 71.
Sum
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Solution
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
⇒ (a + b + c)2 = 83 + 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
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Application of Formulae
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