1.若(z-x)的平方-4(x-y)(y-z)=0则x+z-2y+1999等于.2.因式分解x的4次方+4=需过程

1 (z-x)^2-4(x-y)(y-z)=0
(x+z)^2-4(xy-y^2-xz+yz)-4xz=0
(x+z)^2-4(xy-y^2+yz)=0
(x+z)^2-4y(x+z-y)=0
（x+z-2y)^2=0
x+z=2y
x+z-2y+1999=0+1999=1999
2 x^4+4
=(x^4+4x^2+4)-4x^2
=(x²+2)²-(2x)²
=[(x²+2)+2x][(x²+2)-2x]
=(x²+2x+2)(x²-2x+2)
3 4^m+4^n-4^(m+n+1)/2
=(4^m/2)^2+(4^n/2)^2-2*(4^m/2)(4^n/2)
=(4^m/2-4^n/2)^2≥0
当m≠n
4^m+4^n-4^(m+n+1)/2>0
4 x^4+(1+2+3+4)x^3+(1*2+1*3+1*4+2*3+2*4+3*4)x^2+(1*2*3+1*2*4+2*3*4)x+2*3*4*5
=x^4+10x^3+35x²+50x+24