Question

Find a^3+b^3+c^3 if abc=2,a^2+b^2+c^2=12 and a+b+c=5

Answer 1

a³ + b³ + c³ — 3abc = (a+b+c) ×(a²+b²+c²—ab—bc—ca)
a³+b³+c³ — 6 = 5×(12—13/2)
a³+b³+c³ = 5×(11/2)+6
= 55/2 + 6
= (55+12)/2
= 67/2