Question

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

Answer 1

a^3 + b^3 + c^3 -3abc = (a+b+c)(a^2 + b^2 +c^2 -ab -ca-bc)
Now, first we will find (a+b+c)^2 =a^2 + b^2 +c^2 +2(ab +bc +ca)
(a+b+c)^2= a^2+ b^2 + c^2 +2(10) which is equal to 25 therefore a^2+b^2+^2=5
now put it in the 1st formula
(5){5-(10)}=5×-5=-25
are u sure question doesn't has a -3abc 'cuz we got -25 by including it