Question

数学题，求详细过程，，谢谢

Answer 1

(1)
设两根x1，x2
由韦达定理得：x1+x2=-3，x1x2=m
由题意得：|x1-x2|=5
(x1-x2)²=25
(x1+x2)²-4x1x2=25
(-3)²-4m=25
4m=-16
m=-4
m的值为-4
(2)
设方程两根x1，x2
方程有两实根，判别式△≥0
[-2(m-2)]²-4(m²+4)≥0
m≤0
由韦达定理得：x1+x2=-2(m-2)，x1x2=m²+4
由已知得：x1²+x2²=x1x2+21
(x1+x2)²-2x1x2-x1x2-21=0
(x1+x2)²-3x1x2-21=0
[-2(m-2)]²-3(m²+4)-21=0
m²-16m-17=0
(m-17)(m+1)=0
m=17(舍去)或m=-1
m的值为-1

Answer 2

（1）、△=3²-4m=9-4m
x1-x2=(-3+√△)/2-(-3-√△)/2=2√△/2=√△=5
9-4m=25
9-4m=25
m=-4
（2）、△=2²(m-2)²-4(m²+4)=4(m²-4m+4-4m²-16)=4(-3m²-4m-12)
x1²+x2²-x1x2=21
(x1+x2)²-3(x1*x2)=21
(-2(m-2))²-3*(m²+4)=21
4m²-16m+16-3m²-12=21
m²-16m-17=0
(m-17)(m+1)=0

m=17(与题意不符)
m=-1

Answer 3

x2+3x+m＝0 (令x1大于x2)
x1+x2=-3,x1×x2=m
x1-x2=√(9-4m)
√(9-4m)＝5
9-4m=25
4m=-16
m=-4