If a + b + c = 9 and ab + bc + ca = 23, find the value of a2+b2+c2.
(a+b+c)2=a2+b2+c2+2(ab+bc+ca)⇒ (9)2=a2+b2+c2+2×23⇒ 81=a2+b2+c2+46⇒ a2+b2+c2=81−46=36∴ a2+b2+c2=35