Question

If a² + b² + c² = 250 and ab + bc + ca = 3, find a + b + c.

Answer 1

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`