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，

求x四次方y+2x三次方y²+x²y三次方分之x三次方-xy² 的值

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

Answer 2

25分之15=5分之3=15分之9