<4>. Choose the correct form of the following verbs (To V / V-ing) 1. I don't fancy __________ (go) out tonight. 2. She avoided __________ (tell) him about her plans. 3. I would like __________ (come) to the party with you. 4. He enjoys __________ (have) a bath in the evening. 5. She kept __________ (talk) during the film. 6. I am learning __________ (speak) English. 7. Do you mind __________ (give) me a hand? 8. She helped me __________ (carry) my suitcases. 9. I've finished ___________ (cook) - come and eat! 10. He decided __________ (study) biology. 11. I dislike __________ (wait). 12. He asked __________ (come) with us. 13. I promise __________ (help) you tomorrow. 14. We discussed __________ (go) to the cinema, but in the end we stayed at home. 15. She agreed __________ (bring) the pudding to the dinner. 16. I don't recommend __________ (take) the bus - it takes forever! 17. We hope __________ (visit) Amsterdam next month. 18. She suggested __________ (go) to the museum. 19. They plan __________ (start) college in the autumn. 20. I don't want __________ (leave) yet.

4. He enjoys having a bath in the evening.

3. I would like to come to the party with you.

2. She avoided telling him about her plans.

1. I don't fancy going out tonight.

Để tìm tất cả các giá trị thực của m để phương trình $(m^2 - 4)x^4 + (m - 2)x^2 + 1 = 0$ có đúng hai nghiệm phân biệt, ta có thể giải bằng cách sau:

Gọi $y = x^2$, ta có phương trình $$(m^2 - 4)y^2 + (m - 2)y + 1 = 0$$ Để phương trình trên có đúng hai nghiệm phân biệt thì $\Delta = (m - 2)^2 - 4(m^2 - 4) > 0$.

Giải phương trình $$(m - 2)^2 - 4(m^2 - 4) > 0$$ $$m^2 - 4m + 4 - 4m^2 + 16 > 0$$ $$-3m^2 + 4m + 12 > 0$$ $$3m^2 - 4m - 12 < 0$$ $$m \in \left(-\infty, \frac{4 - \sqrt{4^2 - 4*3*(-12)}}{2*3}\right) \cup \left(\frac{4 + \sqrt{4^2 - 4*3*(-12)}}{2*3}, +\infty\right)$$ $$m \in \left(-\infty, -2\right) \cup \left(\frac{4 + \sqrt{100}}{6}, +\infty\right)$$ $$m \in \left(-\infty, -2\right) \cup \left(\frac{2}{3}, +\infty\right)$$.

Vậy các giá trị của $m$ để phương trình $(m^2 - 4)x^4 + (m - 2)x^2 + 1 = 0$ có đúng hai nghiệm phân biệt là $m \in \left(-\infty, -2\right) \cup \left(\frac{2}{3}, +\infty\right)$.

Đáp án: $m \in \left(-\infty, -2\right) \cup \left(\frac{2}{3}, +\infty\right)$