Question

关于x的一元二次方程x的平方-(m-3)x-2等于0

Answer 1

（1）△=（m-3)²-4(-m²)=m²-6m+9+4m²=5m²-6m+9=5(m-3/5)²-9/5+9=5（m-3/5)²+36/5
∵5（m-3/5)²≥0
∴△=（m-3)²-4(-m²)=5（m-3/5)²+36/5＞0
∴关于x的一元二次方程x²-(m-3)-m²=0有两个不相等的实数根。
（2）∵x1+x2=m-3 | x1| =| x2| -2
x1x2=-m² | x1|- | x2| =-2
∴x1²+x2²+2x1x2=m²-6m+9 | x1|²+ | x2|² -2 | x1|| x2| =4

x1²+x2²-2m²=m²-6n+9 x1 ²+x2²-2 | -m²| =4
x1²+x2²=3m²-6m+9 3m²-6m+9-2m²-4=0
m²-6m+5=0
(m-1)(m-5)=0
m=1或m=5
当m=1时x²+2x-1=0
(x+1)²=2
x1、x2=-1±√2
当m=5时x²-2x-25=0
(x-1)²=26
x1、x2=1±√26

Answer 2

(1)判别式>0与m的值无关
（2）把第二题重新发一遍