Question

if a+b+c=5and ab+bc+ca=100,then prove that a3+b3+c3=3abc=-25

Answer 1

a3+b3+c3-3abc=-25

L.H.S=a3+b3+c3-3abc

(a+b+c)(a2+b2+c2-ab-bc-ca)

5[(a+b+c)2-3(ab+bc+ca)]

5[(5)2 -3(10)]

5(25-30)

5 x -5

-25

R.H.S= -25

L.H.S=R.H.S

Hence Proved