Each of X, Y and Z is a real number that satisfies both of these equations:
X + Y = 2, and:
X*Y - Z² = 1

Find the value of X⁵ + Y⁵ + Z⁵

(In reply to Quick and dirty (spoiler) by Steve Herman)

Yes.

Alternatively: x(2-x)-1 =z^2; -(x-1)^2 = z^2, and z has to be 0, so x is 1. y+1=2 simplifies to y=1.

So x⁵ + y⁵ + z⁵= 2.

Edited on February 1, 2015, 11:34 pm

Posted by broll on 2015-02-01 23:28:57