Question

If a + b + c = 9 and ab + bc + ca = 40, find a² + b² +c².

Answer 1

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