Question

if a+b+c=5and ab+bc+ca=10then prove that,a3+b3+c3-3abc= -25

Answer 1

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