已知x=√3+√2/√3-√2,y=√3-√2/√3+√2,求x^3-xy^2/x^4y+2x^3y^2+x^2y^3
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![已知x=√3+√2/√3-√2,y=√3-√2/√3+√2,求x^3-xy^2/x^4y+2x^3y^2+x^2y^3](/uploads/image/z/1255706-26-6.jpg?t=%E5%B7%B2%E7%9F%A5x%3D%E2%88%9A3%2B%E2%88%9A2%2F%E2%88%9A3-%E2%88%9A2%2Cy%3D%E2%88%9A3-%E2%88%9A2%2F%E2%88%9A3%2B%E2%88%9A2%2C%E6%B1%82x%5E3-xy%5E2%2Fx%5E4y%2B2x%5E3y%5E2%2Bx%5E2y%5E3)
已知x=√3+√2/√3-√2,y=√3-√2/√3+√2,求x^3-xy^2/x^4y+2x^3y^2+x^2y^3
已知x=√3+√2/√3-√2,y=√3-√2/√3+√2,求x^3-xy^2/x^4y+2x^3y^2+x^2y^3
已知x=√3+√2/√3-√2,y=√3-√2/√3+√2,求x^3-xy^2/x^4y+2x^3y^2+x^2y^3
x=√3+√2/√3-√2,y=√3-√2/√3+√2
xy=1
x-y=(√3+√2)/(√3-√2)-(√3-√2)/(√3+√2)=[(√3+√2)²-(√3-√2)²]/(3-2)=4√6
x+y==(√3+√2)/(√3-√2)+(√3-√2)/(√3+√2)=[(√3+√2)²+(√3-√2)²]/(3-2)=10
∴x^3-xy^2/x^4y+2x^3y^2+x^2y^3
=x(x²-y²)/[x²y(x²+2xy+y²)]
=(x+y)(x-y)/[xy(x+y)²]
=(x-y)/[xy(x+y)]
=4√6/(1*10)
=2√6/5
x=√3+√2/√3-√2,y=√3-√2/√3+√2
xy=1
x-y=(√3+√2)/(√3-√2)-(√3-√2)/(√3+√2)=[(√3+√2)²-(√3-√2)²]/(3-2)=4√6
x+y==(√3+√2)/(√3-√2)+(√3-√2)/(√3+√2)=[(√3+√2)²+(√3-√2)²]/(3-2)=10
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x=√3+√2/√3-√2,y=√3-√2/√3+√2
xy=1
x-y=(√3+√2)/(√3-√2)-(√3-√2)/(√3+√2)=[(√3+√2)²-(√3-√2)²]/(3-2)=4√6
x+y==(√3+√2)/(√3-√2)+(√3-√2)/(√3+√2)=[(√3+√2)²+(√3-√2)²]/(3-2)=10
∴x^3-xy^2/x^4y+2x^3y^2+x^2y^3
=x(x²-y²)/[x²y(x²+2xy+y²)]
=(x+y)(x-y)/[xy(x+y)²]
=(x-y)/[xy(x+y)]
=4√6/(1*10)
=2√6/5
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