Question

If a+b+c=10, ab+bc+ca= 24, a^2+b^2+c^2=?

Answer 1

52

Explanation:

Expand the trinomial - if this is confusing you can set

`d=b+c`

And expand
`(a+d)^2`, then substitute the terms back in afterwards.

`(a+b+c)^(2)=100\\ (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca\\100=a^2+b^2+c^2 +2(ab+bc+ca)\\100-2(24)=a^2+b^2+c^2\\100-48=52`