Question

plse solve this...

Answer 1

Just trying out some random values for a, b and c, I'm getting that:

a=2, b=3, and c=5 yields x = -11, y = -1, and z = 19, which makes the expression:\[x^3+y^3+z^3-3xyz=4900=10^2\cdot 7^2\]Notice that a+b+c=10, and x+y+z-7. Changing the value of a to 7 yields:

a=7,b=3, and c=5 yields x= 34, y = -26, z = 4, which makes the expression:\[x^3+y^3+z^3-3xyz=32400 = 15^2\cdot 12^2\]I tried a couple more to see the pattern, wont post those here. It looks like you expression should factor to become:\[x^3+y^3+z^3-3xyz=(a+b+c)^2(x+y+z)^2\]Now all that remains is to show that is indeed true (which I'm working on right now.)

Answer 2

Of course i'll need it all in terms of a,b and c, not x, y and z. But its a start.