SUEC 高中 Adv Maths(Quadratic Inequalities) (Part 2).pptx
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- 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
Editor's Notes
- https://www.toppr.com/ask/content/story/amp/solve-problems-on-inequalities-involving-irrational-functions-70997/