Question

if a+b+c=15 then a^2+b^2+c^2=83 then find the value of a^3+b^3+c^3-3abc

Answer 1

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

We have to find ab+bc+ca
a+b+c = 15
Squaring on both sides
(a+b+c)² = 15²
a²+b²+c²+2(ab+bc+ca) = 225
83+2(ab+bc+ca) = 225
2(ab+bc+ca) = 142
ab+ bc+ca = 71

a³+b³+c³-3abc = (a+b+c) (a²+b²+c²-(ab+bc+ca))
Putting the values
15(83-71)
15×12
180