数学题~(一道数学题,各位数学天才高人智者请多指点!拜托各位大侠啦~~~~~~(>__
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/03 23:20:32
数学题~(一道数学题,各位数学天才高人智者请多指点!拜托各位大侠啦~~~~~~(>__
![数学题~(一道数学题,各位数学天才高人智者请多指点!拜托各位大侠啦~~~~~~(>__](/uploads/image/z/18110718-54-8.jpg?t=%E6%95%B0%E5%AD%A6%E9%A2%98%7E%28%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E5%90%84%E4%BD%8D%E6%95%B0%E5%AD%A6%E5%A4%A9%E6%89%8D%E9%AB%98%E4%BA%BA%E6%99%BA%E8%80%85%E8%AF%B7%E5%A4%9A%E6%8C%87%E7%82%B9%21%E6%8B%9C%E6%89%98%E5%90%84%E4%BD%8D%E5%A4%A7%E4%BE%A0%E5%95%A6%7E%7E%7E%7E%7E%7E%28%3E__)
1. ①
X²-2XY-3Y²=5
X²+2XY+Y²=5+4XY+4Y²
(X+Y)²=5+4Y(X+Y)
4Y=-4
Y= -1
X=2
1. ②
设Z=X-Y
Z²-2Z-3=0
(Z+1)(Z-3)=0
Z=-1 OR Z=3
Z=-1, X-Y=-1
X²-Y²=1, (X+Y)(X-Y)=1
X+Y=-1
X=-1, Y=0
Z=3, X-Y=3
X²-Y²=1, (X+Y)(X-Y)=3
X+Y=1
X=2, Y=-1
2.
x²-(m-2)x-m²/4=0
Δ=(m-2)²-4(-m²/4)=m²-4m+4+m²=(m-2)²+m²>0
因此无论m取何值,Δ始终大于零,这个方程总有两个相异实根.
3.
y=k(x-1), x=4,y=4, -> k=4/3
y=-4, -4=(4/3)(x-1) -> x=-2
X²-2XY-3Y²=5
X²+2XY+Y²=5+4XY+4Y²
(X+Y)²=5+4Y(X+Y)
4Y=-4
Y= -1
X=2
1. ②
设Z=X-Y
Z²-2Z-3=0
(Z+1)(Z-3)=0
Z=-1 OR Z=3
Z=-1, X-Y=-1
X²-Y²=1, (X+Y)(X-Y)=1
X+Y=-1
X=-1, Y=0
Z=3, X-Y=3
X²-Y²=1, (X+Y)(X-Y)=3
X+Y=1
X=2, Y=-1
2.
x²-(m-2)x-m²/4=0
Δ=(m-2)²-4(-m²/4)=m²-4m+4+m²=(m-2)²+m²>0
因此无论m取何值,Δ始终大于零,这个方程总有两个相异实根.
3.
y=k(x-1), x=4,y=4, -> k=4/3
y=-4, -4=(4/3)(x-1) -> x=-2