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> 方程xx-2+12-x=12的解是______;若关于x的方程ax+1x-1-1=0无实根,则a的值为______.-数学
方程xx-2+12-x=12的解是______;若关于x的方程ax+1x-1-1=0无实根,则a的值为______.-数学
题目简介
方程xx-2+12-x=12的解是______;若关于x的方程ax+1x-1-1=0无实根,则a的值为______.-数学
题目详情
方程
x
x-2
+
1
2-x
=
1
2
的解是______;若关于x的方程
ax+1
x-1
-1=0无实根,则a的值为______.
题型:填空题
难度:偏易
来源:不详
答案
方程两边同乘2(x-2),
得2x-2=x-2,
解得x=0.
经检验x=0是原方程的根,
故方程
class="stub"x
x-2
+
class="stub"1
2-x
=
class="stub"1
2
的解是x=0;
(1)x=1为原方程的增根,
此时有ax+1-(x-1)=0,即a+1-(1-1)=0
解得a=-1.
(2)方程两边都乘(x-1),
得ax+1-(x-1)=0,
化简得:(a-1)x=-2.
当a=1时,整式方程无解.
综上所述,当a=±1时,原方程无解.
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题目简介
方程xx-2+12-x=12的解是______;若关于x的方程ax+1x-1-1=0无实根,则a的值为______.-数学
题目详情
答案
得2x-2=x-2,
解得x=0.
经检验x=0是原方程的根,
故方程
(1)x=1为原方程的增根,
此时有ax+1-(x-1)=0,即a+1-(1-1)=0
解得a=-1.
(2)方程两边都乘(x-1),
得ax+1-(x-1)=0,
化简得:(a-1)x=-2.
当a=1时,整式方程无解.
综上所述,当a=±1时,原方程无解.