x+1/x=4=>x=2-3^0.5
=>x^2=4x-1; x^2+1=4x
=>x^4+x^2/(1+x^2)=(4x-1)^2+x^2/(4x)=16x^2-8x+1+x/4=16(4x-1)-8x+1+x/4=225x/4-15=（390-225根号3）/4
-4x平方-9y平方-4x+12y-1=-(2x+1)^2-(3y-2)^2+4
x=-0.5, y=2/3, 最大值=4.