Question

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

Answer 1

a+b+c=5-----(1)
ab+bc+ca=10-----(2)
Do the square of (1)
(a+b+c)2=25

a2+b2+c2+2ab+2bc+2ca=25
a2+b2+c2+2(ab+bc+ca)=25
a2+b2+c2+2×10=25
a2+b2+c2=25-20
a2+b2+c2=5---(3)
Lhs=a3+b3+c3-3abc
=(a+b+c)(a2+b2+c2-ab-bc-ca)+3abc-3abc
=5(5-10)
=5×(-5)
=-25
=Rhs