已知抛物线y=x²+（1-2a）x+a²（a≠0）与x轴交于两点A（x₁，0）、B（x₂，0）（x₁≠x₂）。

（1）求a的取值范围，并证明A、B两点都在原点O的左侧；

（2）若抛物线与y轴交于点C，是否存在这样的a使得OA²+OB²=OA+OB+OC-1成立，若存在，求出a，若不存在，说明理由。

词形变换。

1. The ________ Sunday in May is Mother's Day. (two)

2. The teacher told us not to go ________ alone in the river. (swim)

3. I want to be an ________ when I grow up. (invent)

4. Shouting in public is ________. (polite)

5. We are ________ about the good news. (excite)

6. The ________ we exercise, the healthier we'll get. (much)

7. It is ________ that many drinks are bad for our health. (say)

8. As a student, we should listen to teachers ________. (careful)

9. It is very cold outside. You had better ________ on a coat. (put)

10. He told me he ________ go to the Great Wall tomorrow. (will)