就今天!..因式分解：x^2+4(xy-1)+4y^2x^3+3x-42x^2-3X-1解关于x的方程：(k-2)x^2

x^2+4(xy-1)+4y^2=(x^2+4xy+4y^2)-1=(x+2y)^2-1=(x+2y+1)(x+2y-1)
x^3+3x-4=(x^3-1)+(3x-3)=(x-1)(x^2+x+1)+3(x-1)=(x-1)(x^2+x+4)
2x^2-3x-1=0 x=(3±根号17)/4
2x^2-3x-1=2[x-(3+根号17)/4][x-(3-根号17)/4]
(k-2)x^2+k=(2k-1)x (k-2)x^2-(2k-1)x+k=0
k=0时,-2x^2=-x x(2x-1)=0 x=0或x=1/2
k≠0时,x=[2k-1±根号(4k+1)]/2(k-2)
[x^(1/2)-y^(1/2)]/[x^(1/4)-y^(1/4)]
=[x^(1/4)+y^(1/4)][x^(1/4)-y^(1/4)]/[x^(1/4)-y^(1/4)]=x^(1/4)+y^(1/4)
(a^2+a^-2-2)/(a^2-a^-2)=(a-1/a)^2/[(a+1/a)(a-1/a)]=(a-1/a)/(a+1/a)
=(a^2-1)/(a^2+1)
(8a^-3/27b^6)^(-1/3)={[2a/3b^(-2)]^(-3)}^(-1/3)=2a/3b^(-2)=2ab^2/3
4x^(1/4)[-3x^(1/4)*y^(-1/3)]/[-6x^(-1/2)*y^(-2/3)]
=-2x^[1/4+1/4-(-1/2)]*y^[-1/3-(-2/3)]/3
=-2x^y^(1/3)/3