原式=90^90*(x/90)^90 *6^6(y/6)^6*3^3(z/3)^3*(1-x-y-z)
=90^90*6^6*3^3*(x/90)(x/90)...(x/90)(y/6)...(y/6)(z/3)(z/3)(z/3)(1-x-y-z)
<=90^90*6^6*3^3*[(x/90+x/90+...+x/90+y/6+...+y/6+z/3+z/3+z/3+1-x-y)/100]^100
=09^90*6^*3^3/100^100
等号成立时
=1-x-y-z
x/90=y/6=z/3
所以x=90/99,y=6/99,z=3/99
x=10/11,y=2/33,z=1/33
最大值为90^90*6^*3^3/100^100