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If a^{2} + b^{2} + c^{2} = 250 and ab + bc + ca = 3, find a + b + c.

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#### 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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