不等式|x²-5x+5|＜1的解集是
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解决时间 2021-11-14 20:58
- 提问者网友：泪痣哥哥
- 2021-11-14 07:08
不等式|x²-5x+5|＜1的解集是
最佳答案
- 五星知识达人网友：傲气稳了全场
- 2021-11-14 07:38
|x²-5x+5|＜1
-1
x²-5x+6>0
(x-2)(x-3)>0
x>3或x<2
x²-5x+5<1
x²-5x+4<0
(x-1)(x-4)<0
1
取交集得
{X|1
-1
x²-5x+6>0
(x-2)(x-3)>0
x>3或x<2
x²-5x+5<1
x²-5x+4<0
(x-1)(x-4)<0
1
取交集得
{X|1
全部回答
- 1楼网友：醉吻情书
- 2021-11-14 08:56
1＜x＜2或3＜x＜4
- 2楼网友：山河有幸埋战骨
- 2021-11-14 08:04
x^2-5x+5 =0
x = (5+√5)/2 or (5-√5)/2
case1 x= (5+√5)/2 or (5-√5)/2
L.S =0 < 1 (true)
case 2: x > (5+√5)/2
|x²-5x+5|＜1
x²-5x+5＜1
x^2-5x+4<0
1
case 3: (5-√5)/2
-(x²-5x+5)＜1
x^2-5x+6>0
x<2 or x>3
ie (5-√5)/2
same as case2
slolution
case 1 or case 2 or case3 or case 4
"x = (5+√5)/2 or (5-√5)/2 " or "(5+√5)/2 < x <4" or "(5-√5)/2
x = (5+√5)/2 or (5-√5)/2
case1 x= (5+√5)/2 or (5-√5)/2
L.S =0 < 1 (true)
case 2: x > (5+√5)/2
|x²-5x+5|＜1
x²-5x+5＜1
x^2-5x+4<0
1
case 3: (5-√5)/2
-(x²-5x+5)＜1
x^2-5x+6>0
x<2 or x>3
ie (5-√5)/2
same as case2
slolution
case 1 or case 2 or case3 or case 4
"x = (5+√5)/2 or (5-√5)/2 " or "(5+√5)/2 < x <4" or "(5-√5)/2
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