已知x>0,y.>0,且x+y=1
（1）x^2+y^2≥2xy
2(x^2+y^2)≥(x+y)^2=1
x^2+y^2≥1/2
（2）1/x^2+1/y^2=(x+y)^2/x^2+(x+y)^2/y^2
=2+y^2/x^2+x^2/y^2+2y/x+2x/y
≥2+2√[(y^2/x^2)*(x^2/y^2)]+2√[(2y/x)*(2x/y)]
=2+2+2*2
=8
（3）2/x+3/y=(2x+2y)/x+(3x+3y)/y=2+2y/x+3x/y+3
=5+2y/x+3x/y
≥5+2√[(2y/x)*(3x/y)]
=5+2√6
（4）(x+1/x)*（y+1/y）=xy+x/y+y/x+1/xy
= xy + 1/(xy) + (x^2+y^2)/(xy)
= xy + 1/(xy) + (x^2+2xy+y^2)/(xy) -2
= xy + 1/(xy) + (x+y)^2/(xy) -2
= xy + 2/(xy) -2
求 f(z) = z + 2/z 的最小值,其中z=xy