What is x + y + z if the following are true:

x⁴ + y⁴ + z⁴ = 11
x³ + y³ + z³ = 7
x² + y² + z² = 3

Just think of this problem as the reverse of this one.

Square equation 3, subtract equation 1 and divide by 2.

This gives (x^2)(y^2) + (x^2)(z^2) + (y^2)(z^2) = -1.

So, there are no real solutions to this set of equations.

Posted by Steve Herman on 2007-08-25 21:19:16