Question

find the value of a^3+b^3+c^3-3abc if a+b+c=10 and a^2+b^2+c^2=83

Answer 1

We know that (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca) 
So 15^2 = 83 + 2(ab + bc + ca) 
=> 2(ab + bc + ca) = 15^2 - 83 = 225 - 83 = 142 
So ab + bc + ca = 71 

Now, you can factorise 
a^3 + b^3 + c^3 - 3abc as 
(a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca) 
= 15(83 - 71) 
= 15 * 12 
= 180