一元二次方程30道例题

以下是一元二次方程的30道例题，涵盖了各种题型和解法：

1. 解方程：x2 5x + 6 = 0

2. 解方程：2x2 8x + 4 = 0

3. 解方程：x2 + 4x 12 = 0

4. 解方程：x2 3x 10 = 0

5. 解方程：x2 + 6x + 9 = 0

6. 解方程：2x2 5x 3 = 0

7. 解方程：x2 4x 5 = 0

8. 解方程：3x2 12x + 9 = 0

9. 解方程：x2 + 2x 15 = 0

10. 解方程：x2 2x 3 = 0

11. 解方程：2x2 3x 2 = 0

12. 解方程：x2 + 5x + 6 = 0

13. 解方程：x2 7x + 12 = 0

14. 解方程：x2 + 4x 1 = 0

15. 解方程：x2 8x + 16 = 0

16. 解方程：3x2 6x 9 = 0

17. 解方程：x2 + 7x + 12 = 0

18. 解方程：x2 5x + 6 = 0

19. 解方程：2x2 4x 2 = 0

20. 解方程：x2 + 3x 4 = 0

21. 解方程：x2 2x 1 = 0

22. 解方程：3x2 4x + 4 = 0

23. 解方程：x2 + 6x + 5 = 0

24. 解方程：2x2 5x + 2 = 0

25. 解方程：x2 6x + 9 = 0

26. 解方程：3x2 7x + 2 = 0

27. 解方程：x2 + 5x 6 = 0

28. 解方程：2x2 6x + 5 = 0

29. 解方程：x2 + 4x 7 = 0

30. 解方程：3x2 2x 1 = 0

解答过程如下：

1. (x 2)(x 3) = 0，解得 x1 = 2，x2 = 3

2. x = (8 ± √(82 4×2×4)) / (2×2)，解得 x1 = 2，x2 = 1

3. (x 2)(x + 6) = 0，解得 x1 = 2，x2 = -6

4. (x 5)(x + 2) = 0，解得 x1 = 5，x2 = -2

5. (x + 3)2 = 0，解得 x1 = x2 = -3

6. (2x + 1)(x 3) = 0，解得 x1 = -1/2，x2 = 3

7. (x 5)(x + 1) = 0，解得 x1 = 5，x2 = -1

8. (x 3)2 = 0，解得 x1 = x2 = 3

9. (x + 5)(x 3) = 0，解得 x1 = -5，x2 = 3

10. (x + 5)(x 3) = 0，解得 x1 = -5，x2 = 3

11. (2x 1)(x + 2) = 0，解得 x1 = 1/2，x2 = -2

12. (x + 2)(x + 3) = 0，解得 x1 = -2，x2 = -3

13. (x 4)(x 3) = 0，解得 x1 = 4，x2 = 3

14. x = (-4 ± √(42 4×1×(-1))) / (2×1)，解得 x1 = -2 + √5，x2 = -2 √5

15. (x 4)2 = 0，解得 x1 = x2 = 4

16. (x 3)2 = 0，解得 x1 = x2 = 3

17. (x + 4)(x + 1) = 0，解得 x1 = -4，x2 = -1

18. (x 2)(x 3) = 0，解得 x1 = 2，x2 = 3

19. (2x 1)(x 1) = 0，解得 x1 = 1/2，x2 = 1

20. (x + 4)(x 1) = 0，解得 x1 = -4，x2 = 1

21. (x + 1)2 = 0，解得 x1 = x2 = -1

22. (3x 2)2 = 0，解得 x1 = x2 = 2/3

23. (x + 1)(x + 5) = 0，解得 x1 = -1，x2 = -5

24. (2x 1)(x 1) = 0，解得 x1 = 1/2，x2 = 1

25. (x 3)2 = 0，解得 x1 = x2 = 3

26. (3x 1)(x 2) = 0，解得 x1 = 1/3，x2 = 2

27. (x + 2)(x 3) = 0，解得 x1 = -2，x2 = 3

28. (2x 1)(x 5/2) = 0，解得 x1 = 1/2，x2 = 5/2

29. x = (-4 ± √(42 4×1×(-7))) / (2×1)，解得 x1 = -2 + √5，x2 = -2 √5

30. (3x + 1)(x 1) = 0，解得 x1 = -1/3，x2 = 1