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Question
If a2 + b2 + c2 = 250 and ab + bc + ca = 3, find a + b + c.
Solution
Recall the formula
`(a+b+c)^2 = a^2 +b^2 +c^2 + 2(ab + bc + ca)`
Given that
`a^2 + b^2 + c^2 = 250 , ab + bc + ca = 3 `
Then we have
`(a+b+c)^2 = a^2 + b^2 + c^2 + 2 (ab + bc+ca)`
`(a+b+c)^2 = 250 + 2.(3)`
`(a+b+c)^2 = 256`
`(a+b+c) =± 16`
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