Question

If a+b+c=5 and ab + bc+ ca=10,then prove that a 3 +b 3 +c 3 -3abc = -25

Answer 1

a³+b³+c³–3abc = (a+b+c) (a²+b²+c²–(ab+bc+ca))
= (a+b+c) ((a+b+c)²–3(ab+bc+ca))
= 5×(5²–3×10)
= 5×(–5)
= –25