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SUEC 高中 Adv Maths (Inequalities).pptx
- 1. 𝒑𝒈 𝟔𝟕 − 𝟔𝟖 < > < > <
- 2. 𝒑𝒈 𝟔𝟖
- 3. 𝒑𝒈 𝟔𝟖
- 4. 𝒑𝒈 𝟔𝟗
- 5. 𝒑𝒈 𝟔𝟗
- 6. 𝒑𝒈 𝟕𝟎
- 7. 𝒑𝒈 𝟕𝟒
- 8. 𝒑𝒈 𝟕𝟎 − 𝟕𝟏
- 9. 𝒑𝒈 𝟕𝟒
- 10. 𝒑𝒈 𝟕𝟒 4 + 𝑎2 − 4𝑎 = 𝑎2 −4𝑎 + 4 = 𝑎2 −4𝑎 + 22 − 22 + 4 = (𝑎 − 2)2 (𝑎 − 2)2 ≥ 0 ∴ 4 + 𝑎2 > 4𝑎 1 > 4𝑎 4 + 𝑎2 4𝑎 4 + 𝑎2 < 1 (𝑥 + 𝑦) 1 𝑥 + 1 𝑦 − 4 = 1 + 𝑥 𝑦 + 𝑦 𝑥 + 1 − 4 = 𝑥 𝑦 + 𝑦 𝑥 − 2 = 𝑥2 + 𝑦2 − 2𝑥𝑦 = 𝑥 − 2 (𝑥 − 𝑦)2≥ 0 ∴ (𝑥 + 𝑦) 1 𝑥 + 1 𝑦 > 4
- 11. 𝒑𝒈 𝟕𝟏 − 𝟕𝟐
- 12. 𝒑𝒈 𝟕𝟐
- 13. 𝒑𝒈 𝟕𝟑
- 14. 𝒑𝒈 𝟕𝟑
- 15. 𝒑𝒈 𝟕𝟑
- 16. 𝒑𝒈 𝟕𝟒
- 17. 𝒑𝒈 𝟕𝟒 𝑎 𝑏 + 𝑏 𝑐 + 𝑐 𝑎 ≥ 3 − −① 𝑏 𝑎 + 𝑐 𝑏 + 𝑎 𝑐 ≥ 3 − −② ① × ② 𝑎 𝑏 + 𝑏 𝑐 + 𝑐 𝑎 𝑏 𝑎 + 𝑐 𝑏 + 𝑎 𝑐 ≥ 9 𝑥3 + 4 2𝑥2 2 ≥ 4 𝑥 𝑥6 + 8𝑥3 + 16 4𝑥4 ≥ 4 𝑥 𝑥7 + 8𝑥4 + 16𝑥 ≥ 16𝑥4 𝑥7 − 8𝑥4 + 16𝑥 ≥ 0 𝑥(𝑥6 − 8𝑥3 + 16) ≥ 0 𝑥(𝑥3 − 4)2 ≥ 0 𝑥 ≥ 0 𝑜𝑟 𝑥 ≥ 3 4 𝑥 + 4 𝑥2 ≥ 4 𝑥 𝑥 + 4 𝑥2 ≥ 4 5 4 𝑥 + 4 𝑥2 ≥ 3
- 18. 𝒑𝒈 𝟕𝟒
- 19. 𝒑𝒈 𝟕𝟒 𝑎2 + 𝑏2 + 𝑐2 + 𝑑2 ≥ 4 𝑎2𝑏2𝑐2𝑑2 − −① 1 𝑎2 + 1 𝑏2 + 1 𝑐2 + 1 𝑑2 ≥ 4 1 𝑎2𝑏2𝑐2𝑑2 − −② ① × ② 𝑎2 + 𝑏2 + 𝑐2 + 𝑑2 1 𝑎2 + 1 𝑏2 + 1 𝑐2 + 1 𝑑2 ≥ 16
- 20. 𝒑𝒈 𝟕𝟓 − 𝟕𝟕
- 21. 𝒑𝒈 𝟕𝟔
- 22. 𝒑𝒈 𝟕𝟔 − 𝟕𝟕
Editor's Notes
- https://www.mathsisfun.com/algebra/inequality-properties.html
- https://www.mathsisfun.com/algebra/inequality-properties.html
- https://www.mathsisfun.com/algebra/inequality-properties.html
- https://www.mathsisfun.com/algebra/inequality-properties.html