Question

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

Answer 1

From L. H. S, a^3+b^3+c^3-3abc=(a+b+c) (a^2+b^2+c^2-ab-bc-ca)
=(5) [(a+b+c)^2 -2ab-2bc-2ca -ab-bc-ca]
=(5) [(5)^2 -2(ab+bc+ca) -(ab+bc+ca)]
=(5) [25 -2*10 -10]
=(5) [25-20-10]
=(5) [25-30]
=5*-5
=-25.
Hence, L.H.S=R.H.S