3.7 解一元高次方程式 Solve Higher-order Equation in One Variable - 练习题 - 独中课程 | 线上补习

高中一 | 高级数学

About Lesson

Solve the following equations:
解下列方程式：

1. $x^3 - 12x + 16 = 0$

2. $x^3 - 2x^2 + 5x - 4 = 0$

3. $2x^3 + 5x^2 + x - 2 = 0$

4. $4x^4 - 4x^3 + 7x^2 + x - 2 = 0$

5. $2x^5 - 5x^4 - 7x^3 + 4x^2 + 5x + 1 = 0$

6. $(x + 1)^3 - 4(x + 1)^2 - 9(x + 1) - 4 = 0$ [bg_collapse view=”link” color=”#c4255a” expand_text=”Hint” collapse_text=”Close Hint” ]设 $y = x + 1$ [/bg_collapse]

7. $3(x^2 + x)^2 - 7(x^2 + x) + 2 = 0$ [bg_collapse view=”link” color=”#c4255a” expand_text=”Hint” collapse_text=”Close Hint” ]设 $y = x^2 + x$ [/bg_collapse]

8. $(x + 1)(x + 3)(x - 2)(x - 4) = 24$ [bg_collapse view=”link” color=”#c4255a” expand_text=”Hint” collapse_text=”Close Hint” ]配对相乘，设 $y = x^2 - x$ [/bg_collapse]

9. $(x - 1)(x - 2)(x + 3)(x + 4) = 36$ [bg_collapse view=”link” color=”#c4255a” expand_text=”Hint” collapse_text=”Close Hint” ]配对相乘，设 $y = x^2 + 2x$ [/bg_collapse]

10. $(x - 1)(x - 2)(2x + 1)(2x + 3) = 6$ [bg_collapse view=”link” color=”#c4255a” expand_text=”Hint” collapse_text=”Close Hint” ]配对相乘，设 $y = 2x^2 - x$ [/bg_collapse]

11. $(x^2 - x - 6)(x^2 + 3x - 4) + 24 = 0$ [bg_collapse view=”link” color=”#c4255a” expand_text=”Hint” collapse_text=”Close Hint” ]将两个式子因式分解后再配对相乘，设 $y = x^2 + x$ [/bg_collapse]

12. $2x^4 + x^3 - 11x^2 + x + 2 = 0$ [bg_collapse view=”link” color=”#c4255a” expand_text=”Hint” collapse_text=”Close Hint” ]可用综合除法或倒数方程式方法[/bg_collapse]

13. $4x^4 - 4x^3 - 7x^2 - 4x + 4 = 0$ [bg_collapse view=”link” color=”#c4255a” expand_text=”Hint” collapse_text=”Close Hint” ]可用综合除法或倒数方程式方法[/bg_collapse]

14. $x^4 + 3x^3 - 8x^2 + 3x +1 = 0$ [bg_collapse view=”link” color=”#c4255a” expand_text=”Hint” collapse_text=”Close Hint” ]可用综合除法或倒数方程式方法[/bg_collapse]

15. $2x^5 - x^4 + 2x^3 + 2x^2 - x + 2 = 0$ [bg_collapse view=”link” color=”#c4255a” expand_text=”Hint” collapse_text=”Close Hint” ]先综合除法先得解1后，再用倒数方程式方法，可是都没有实根[/bg_collapse]

16. $x^5 + x^4 - 3x^3 + 3x^2 - x- 1 = 0$ [bg_collapse view=”link” color=”#c4255a” expand_text=”Hint” collapse_text=”Close Hint” ]先综合除法先得解1后，再用倒数方程式方法[/bg_collapse]