+0

# Problem

+1
680
2
x-y=3 then x^3-y^3-9xy =?
Jan 14, 2016

#1
+6

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.

Jan 14, 2016

#1
+6

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.

Guest Jan 14, 2016
#2
+5

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!

Jan 15, 2016