若|X+Y-4|+(XY-1)^2=0,则X^2+Y^2=__________

问题描述:

若|X+Y-4|+(XY-1)^2=0,则X^2+Y^2=__________

|X+Y-4|+(XY-1)^2=0
得到X+Y=4
XY=1
X^2+Y^2=(X+Y)^2-2XY=16-2=14