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Question
If a + b + c = 11 and a2 + b2 + c2 = 81, find : ab + bc + ca.
Sum
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Solution
Since (a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)
∴ (11)2 = 81 + 2 (ab + bc + ca)
∴ 2(ab + bc + ca) = 121 − 81 = 40
ab + bc + ca = `40/2`
⇒ ab + bc + ca = 20
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