Question

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

Answer 1

if a + b + c = 5
(a + b + c )^2=25
a ^2+ b ^2+ c ^2+2 (ab + bc +ca)=25
a ^2+ b ^2+ c ^2=25-2*10=5
a cube + b cube + c cube-3abc
=(a + b + c)(a ^2+ b ^2+ c ^2-ab - bc -ca)
=5*(5_10)
=5*(-5)
=-25