If a + b + c =11 and ab + bc + ac = 25,then find the value of a^3 + b^3 + c^3 – 3abc
Notice that a3+b3+c3−3abc=(a+b+c)(a2+b2+c2−(ab+bc+ca))
The only missing info we need is the value of a2+b2+c2.
Now, because (a+b+c)2=a2+b2+c2+2(ab+bc+ca), plugging in values gives a2+b2+c2=112−2(25)=71
You can plug in the values on your own.
so like what maxwong said we have a^2+b^2+c^2=71 and a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - (ab + bc +ca)) plug that in to get 11*(71-25) and that equals 506.
Credts: Maxwong for hints