ab+bc+ca when a+b+c =13 and a2+b2+c2=69

Question

find a2+b2+c2=69

Answer 1

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

2(ab + bc + ca) = (a + b + c)^2  -  (a^2 + b^2 + c^2) = 169 - 69 = 100.

(ab + bc + ca) = 50.