Question

If a + b + c = 9 and ab + bc + ca = 23, find the value of a² + b² + c².

Answer 1

We know that,

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

`=> (9)^2 = a^2 + b^2 + c^2 + 2(23)`

`=> 81 = a^2 + b^2 + c^2 + 46`       [∵ a + b + c = 9 and (ab + bc + ca = 23)]

`=> a^2 + b^2 + c^2 = 81 - 46`

`=> a^2 + b^2 + c^2 = 35`