Question

已知：x=根号3-根号2分之根号3+根号2,y=根号3+根号2分之根号3-根号2,

Answer 1

x=(√3+√2)/(√3-√2)=(√3+√2)^2/(3-2)=(√3+√2)^2

同理 y＝（√3-√2）^2

xy=(√3+√2)^2(√3-√2)^2=(3-2)^2=1

x-y=(√3+√2)^2-(√3-√2)^2=4√3x√2=4√6

x+y=(√3+√2)^2+(√3-√2)^2=2x3+2x2=10

(x^3-xy^2)/(x^4y+2x^3y^2+x^2y^3)

=(x^2-y^2)/(x^3y+2x^2y^2+xy^3)

=(x^2-y^2)/xy(x^2+2xy+y^2)

=(x+y)(x-y)/xy(x+y）^2

=(x-y)/xy(x+y)

=(x-y)/(x+y)

=4√6/10

=2/5√6