已知x=根号2-根号3/根号3+根号2,y=根号3+根号2/根号3-根号2,那么代数式3x^2-5xy+3y^2的值是?

x=(根号2-根号3)/(根号3+根号2)
=(根号2-根号3)*(根号3-根号2)/((根号3+根号2)*(根号3-根号2))
=(-5+2根号6)/(3-2)
=-5+2根号6
y=(根号3+根号2)/(根号3-根号2)
=(根号3+根号2)*(根号3+根号2)/(根号3-根号2)*(根号3+根号2))
=(5+2根号6)/(3-2)
=5+2根号6
x*y=(根号2-根号3)/(根号3+根号2)*(根号3+根号2)/(根号3-根号2)
=-1
3x^2-5x*y+3y^2
=3(x^2-2x*y+y^2)+x*y
=3(x-y)^2+x*y
=3(-5+2根号6-(5+2根号6))^2+(-1)
=3(-5+2根号6-5-2根号6)^2+(-1)
=3(-10)^2-1
=300-1
=299