Question

Find the largest possible value of x^3+y^3+z^3 for realx, y, z, such that
xyz^2=−64y−128x
x^2yz=−32y−32z
3xy^2z=128x−64z

Answer 1

My answer is 440

My way of solving:
xyz(z)=−64y−128x (1)
xyz(x)=−32y−32z (2)
3xyz(y)=128x−64z (3)

(1)-(2)
xyz(z-2x)=64(z-2x)
xyz=64 ,z=2x
if z=2x,x=y=z=0
if xyz=64,
sub xyz=64 into (1),(2),(3)
simplify it and you can get:
z=-y-2x (4)
2x=-y-z (5)
3y=2x-z (6)

(5)=(6)because xyz=64 is derived from (1)and(2)

equate it and you will get:
y=2x,z=-4x

x^3+y^3+z^3=-55x^3=440

Answer 2

thanks