当x=0.3,y=0.7时,求分式x^3-x^2-xy^2+y^3/-x^4+2x^2y^2-y^4的值,
问题描述:
当x=0.3,y=0.7时,求分式x^3-x^2-xy^2+y^3/-x^4+2x^2y^2-y^4的值,
答
x^3-x^2-xy^2+y^3/-x^4+2x^2y^2-y^4=[(x^3+y^3)-xy(x+y)]/[-(x^2-y^2)^2]=[(x+y)(x^2-xy+y^2)-xy(x+y)]/[-(x^2-y^2)^2]=[x^2-2xy+y^2]/[-(x^2-y^2)^2]=-(x-y)^2/(x-y)^2(x+y)^=-1/(x+y)^2=-1