Sources: Visual - various maths sites (credits to original creator) Questions - Dong Zong's Textbook

1. 𝒑𝒈 𝟖𝟔 − 𝟖𝟕

2. 𝒑𝒈 𝟖𝟕

3. 𝒑𝒈 𝟖𝟖

4. 𝒑𝒈 𝟖𝟗

5. 𝒑𝒈 𝟖𝟖

6. 𝒑𝒈 𝟖𝟗

7. 𝒑𝒈 𝟖𝟗
3𝑥 + 1 ≥ 0
2𝑥 + 1 ≥ 0
𝑥 ≥ −
1
3
𝑥 ≥ −
1
2
𝑥 ≥ −
1
3
3𝑥 + 1 > 2𝑥 + 1 − 2 2𝑥 + 1 + 1
𝑥 − 1 > −2 2𝑥 + 1
𝑥2
− 2𝑥 + 1 > 4(2𝑥 + 1)
𝑥2 − 10𝑥 − 3 > 0
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑥 =
10 ± 102 − 4(1)(−3)
2(1)
𝑥 = 5 ± 2 7
𝑥 > 5 − 2 7 𝑜𝑟 𝑥 > 5 + 2 7
−
1
3
5 − 2 7 5 + 2 7

8. 𝒑𝒈 𝟖𝟖 − 𝟖𝟗

9. 𝒑𝒈 𝟖𝟗

10. 𝒑𝒈 𝟗𝟎 − 𝟗𝟏

11. 𝒑𝒈 𝟗𝟏

12. 𝒑𝒈 𝟗𝟏

13. 判别式 𝒑𝒈 𝟓𝟐
complex
∆
2 equal roots
有两不等实根
无实根 有两相等实根

14. 𝒑𝒈 𝟗𝟐 ∆ = 𝒃𝟐 − 𝟒𝒂𝒄

15. 𝒑𝒈 𝟗𝟑 ∆ = 𝒃𝟐 − 𝟒𝒂𝒄

16. 𝒑𝒈 𝟗𝟑 ∆ = 𝒃𝟐 − 𝟒𝒂𝒄

17. 𝒑𝒈 𝟗𝟑
∆ = 𝒃𝟐
− 𝟒𝒂𝒄 ≥ 𝟎
𝐿𝑒𝑡 𝑦 =
𝑥4 − 𝑥2 + 4
𝑥2
𝑦𝑥2
= 𝑥4
− 𝑥2
+ 4
𝑥4
− 𝑥2
− 𝑦𝑥2
+ 4 = 0
𝐿𝑒𝑡 𝑧 = 𝑥2
𝑧2
+ (−1−)𝑧 + 4 = 0
(−1 − 𝑦)2
−4(1)(4) ≥ 0
𝑦2
+ 2𝑦 + 1 − 16 ≥ 0
𝑦2
+ 2𝑦 − 15 ≥ 0
(𝑦 + 5)(𝑦 − 3) ≥ 0
𝑦 ≤ −5 𝑜𝑟 𝑦 ≥ 3
𝑤ℎ𝑒𝑛 𝑦 = −5, 𝑧 = −2, 𝑥 𝑖𝑛𝑣𝑎𝑙𝑖𝑑
𝑤ℎ𝑒𝑛 𝑦 = 3, 𝑧 = 2, 𝑥 = ± 2

18. 𝒑𝒈 𝟗𝟑 ∆ = 𝒃𝟐 − 𝟒𝒂𝒄

19. 𝒑𝒈 𝟗𝟑
𝑎 + 𝑏 = 20
𝑏 = 20 −
𝑎2 + 𝑏2
= 𝑎2
+ 20 − 2
= 𝑎2 +400 − 40𝑎 + 𝑎2
= 2𝑎2
−40𝑎 + 400
= 2(𝑎2 −20𝑎 + 200)
= 2 𝑎2 − 20𝑎 + 100 − 100 + 200
= 2 𝑎 − 10 2
+ 200