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