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> 若关于x的方程2kx-1-xx2-x=kx+1x只有一个解(相等的解也算作一个),试求k的值与方程的解.-数学
若关于x的方程2kx-1-xx2-x=kx+1x只有一个解(相等的解也算作一个),试求k的值与方程的解.-数学
题目简介
若关于x的方程2kx-1-xx2-x=kx+1x只有一个解(相等的解也算作一个),试求k的值与方程的解.-数学
题目详情
若关于x的方程
2k
x-1
-
x
x
2
-x
=
kx+1
x
只有一个解(相等的解也算作一个),试求k的值与方程的解.
题型:解答题
难度:中档
来源:不详
答案
原方程化为kx2+(2-3k)x-1=0①.
(1)当k=0时,原方程有一个解,x=
class="stub"1
2
;
(2)当k≠0时,方程①△=5k2+4(k-1)2>0,总有两个不同的实数根,
由题意知必有一个根是原方程的增根,从原方程知增根只能是0或1,显然0不是①的根,
故x=1,得k=
class="stub"1
2
.
综上可知当k=0时,原方程有一个解,x=
class="stub"1
2
;
k=
class="stub"1
2
时,x=-2.
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题目简介
若关于x的方程2kx-1-xx2-x=kx+1x只有一个解(相等的解也算作一个),试求k的值与方程的解.-数学
题目详情
答案
(1)当k=0时,原方程有一个解,x=
(2)当k≠0时,方程①△=5k2+4(k-1)2>0,总有两个不同的实数根,
由题意知必有一个根是原方程的增根,从原方程知增根只能是0或1,显然0不是①的根,
故x=1,得k=
综上可知当k=0时,原方程有一个解,x=
k=