第1个回答 2021-07-14
四个根分别是x=1±√1-m以及x=1±√1-n。不妨假设m>n，那么n=7/16时，有最小根1/4，最大根7/4，四个根是等差数列，则其他两根是3/4，5/4，算得m=15/16，从而|m-n|=1/2。本回答被网友采纳
第2个回答 2021-07-14
(x^2-2x+m)(x^2-2x+n)=0
4个根
1/4,1/4+d, 1/4+2d, 1/4+3d
f(x)=(x^2-2x+m)(x^2-2x+n)
4根相加
1+6d = 2+2
6d = 3
d=1/2
4个根 : 1/4 , 3/4 , 5/4, 7/4
4根相乘
(1/4)(3/4)(5/4)(7/4) = mn
mn=105/256
f(x)
=(x^2-2x+m)(x^2-2x+n)
=(x-1/4)(x-3/4)(x-5/4)(x-7/4)
=[(x-1/4)(x-7/4)][(x-3/4)(x-5/4)]
=(x^2-2x+7/16)(x-2x+15/16)
|m-n|^2
= (m-n)^2
= (m+n)^2 - 4mn
=(7/16+15/16)^2 - 4(105/256)
= 484/256 -420/256
=64/256
=1/4
|m-n| =1/2
4个根
1/4,1/4+d, 1/4+2d, 1/4+3d
f(x)=(x^2-2x+m)(x^2-2x+n)
4根相加
1+6d = 2+2
6d = 3
d=1/2
4个根 : 1/4 , 3/4 , 5/4, 7/4
4根相乘
(1/4)(3/4)(5/4)(7/4) = mn
mn=105/256
f(x)
=(x^2-2x+m)(x^2-2x+n)
=(x-1/4)(x-3/4)(x-5/4)(x-7/4)
=[(x-1/4)(x-7/4)][(x-3/4)(x-5/4)]
=(x^2-2x+7/16)(x-2x+15/16)
|m-n|^2
= (m-n)^2
= (m+n)^2 - 4mn
=(7/16+15/16)^2 - 4(105/256)
= 484/256 -420/256
=64/256
=1/4
|m-n| =1/2
第3个回答 2021-07-15
根据韦达定理：x1+x2=2=x3+x4=2，又是首项是1/4的等差数列，所以有
x1，x3，x4，x2=1/4，3/4，5/4，7/4
m=1/4×7/4
n=3/4×5/4
|m-n|=8/16=1/2
当然反之也成立。
x1，x3，x4，x2=1/4，3/4，5/4，7/4
m=1/4×7/4
n=3/4×5/4
|m-n|=8/16=1/2
当然反之也成立。