x-y=3 then x^3-y^3-9xy =?
There are infinitely MANY solutions to this problem, as long as the difference between x and y=3, then the answer is ALWAYS the same=27. If x=10, y=7, then the answer is 27. This remains true for any positive values of x,y separated by 3.
+118608 Thanks Guest :))
x-y=3 then x^3-y^3-9xy =?
This is fascinating. Look at this weird graph!
https://www.desmos.com/calculator/dbawqgablq
Now for the algebra.
x-y=3
so
y=x-3
Find what x^3-y^3-9xy =
\(x^3-y^3-9xy\\ =x^3-(x-3)^3-9*x(x-3)\\ =x^3-[x^3-3(x^2*3)+3(x*3^2)-3^3]-9x(x-3)\\ =x^3-[x^3-9x^2+27x-27]-9x^2+27x\\ =x^3-x^3+9x^2-27x+27-9x^2+27x\\ =9x^2-27x+27-9x^2+27x\\ =27 \)
Cool!
