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If a + b + c = 9 and ab + bc + ca = 40, find a^{2} + b^{2} +c^{2}.

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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+b+c) = 9,ab + bc + ca = 40`,

Then we have

`(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)`

` ( 9)^2 = a^2 + b^2 + c^2 + 2.( 40) `

`a^2 ++ b^2 + c^2 + 80 = 81`

`a^2 + b^2 + c^2 = 81 - 80

`a^2 + b^2 +c^2 =` **1**

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