X+Y=1，证（1+1/X）乘（1+1/Y）大于等于9

X+Y=1，证（1+1/X）乘（1+1/Y）大于等于9
证明: （1+1/X）（1+1/Y）=1+1/x+1/y+1/(xy)
>=1+4/(2√(xy))+4/(2√(xy))^2
>=1+4/(x+y)+4/(x+y)^2
=1+4+4
=9

2.（X+1/X）平方+（Y+1/Y）平方大于等于25/2
证明.(X+1/X)^2+(Y+1/Y)^2>=2(x+1/x)(y+1/y)
=2[xy+x/y+y/x+1/(xy)]
>=2[xy+2+1/(xy)]
=2[(xy+1/(16xy))+15/(16xy)]+4
>=2[2*1/4+15/4]+4 ( 因为xy<=(x+y)^2/4=1//4)
=25/2