已知关于x的方程（k-1）x2-6x+9=0．
（1）若方程有实数根，求k的取值范围；
（2）若方程有两个不相等的实数根，求k的取值范围；
（3）若方程有两个相等的实数根，求k的值，并求此方程的根．
（1）若k=1，方程为一元一次方程，有解，满足题意；
若k≠1，方程为一元二次方程，
∵方程有实数根，
∴△=b2-4ac=（-6）2-36（k-1）=72-36k≥0，
解得：k≤2且k≠1，
综上，k的范围为k≤2；
（2）∵方程有两个不相等的实数根，
∴△=b2-4ac=（-6）2-36（k-1）=72-36k＞0，且k-1≠0，
解得：k＜2且k≠1；
（3）∵方程有两个相等的实数根，
∴△=b2-4ac=（-6）2-36（k-1）=72-36k=0，且k-1≠0，
解得：k=2．
∴原方程为x2-6x+9=0，
解得x1=x2=3．
| 根据短文内容，用方框中所给的单词填空。 | |
the Asian record with a time of 6'39"71. His fans came to 2 him and asked him whether he liked skating when he was very young. Then he told 3 a story. "In fact,I didn't like skating at all when I was young. On a winter day in December,it snowed 4 and the weather got very cold. I didn't. know how to spend my Saturday. Then I turned on the TV and saw some 5 skating on the lake. I thought, "They're really cool! I will start to skate, too. " Then I put on my coat, took my brother's skating shoes and went out. " "I learned very quickly. A month later, I could skate very well. From then on, I liked it very much. " |