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Question
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
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Solution
We know that,
`(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)`
`=> (0)^2 = 16 + 2(ab + bc + ca)` `[∵ a + b + c = and a^2 + b^2 + c^2 = 16] `
=> 2(ab + bc + ca) = -16
=> ab + bc + ca = -8
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