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=0
x+y=4
XY-1=0
xy=1
(x+y)^2=x^2+2xy+y^2=16
x^2+y^2=16-2xy=16-2=14

x^2+y^2=(x+y)^2-2xy=16-2=14

|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

等于14