Question

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?

Answer 1

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