已知x1,x2是关于x的一元二次方程4kx^2-4kx+k+1=0的两个实数根

x1,x2是关于x的方程4kx^2-4kx+k+1=0的两个实根.
则：x1+x2=-(-4k)/4k=1
x1x2=(k+1)/4k

1)
(2x1-x2)(x1-2x)=2x1^2+2x2^2-5x1x2=2(x1+x2)^2-9x1x2=2-9(k+1)/4k=-3/2
9(k+1)/4k=7/2
9(k+1)=14k
k=9/5
2)
x1/x2+x2/x1-2
=(x1^2+x2^2)/x1x2-2
=(x1+x2)^2/x1x2-4
=4k/(k+1)-4
=-4/(k+1)为整数
则：k=3,1,0,-2,-3,-5
3)
k=-2,方程化为：-8x^2+8x-1=0
8x^2-8x+1=0
x1,2=(2±√2)/4
x1/x2=(2+√2)/(2-√2)=(2+√2)^2/2=3+2√2,或
x1/x2=(2-√2)/(2+√2)=(2-√2)^2/2=3-2√2,

x1,x2是关于x的方程4kx^2-4kx+k+1=0的两个实根.
则：x1+x2=-(-4k)/4k=1
x1x2=(k+1)/4k

1)
(2x1-x2)(x1-2x)=2x1^2+2x2^2-5x1x2=2(x1+x2)^2-9x1x2=2-9(k+1)/4k=-3/2
9(k+1)/4k=7/2
9(k+1)=14k
k=9/5

方程有两个解
则16k^2-16k(k+1)>=0
k^2-k^2-k>=0
k<=0

x1+x2=1,x1*x2=(k+1)/4k

x1/x2+x2/x1-2
=(x1^2+x2^2)/x1*x2-2
=[(x1+x2)^2-2x1x2]/x1*x2-2
=(x1+x2)^2/x1*x2-2-2是整数
则(x1+x2)^2/x1*x2是整数

(x1+x2)^2/x