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SUEC 高中 Adv Maths (2 Roots Part 2)
- 1. 𝒑𝒈 𝟕𝟓 𝒂 = 𝟏 𝒃 = −𝟗 𝐜 = 𝒎 ∝ + 𝜷 = − 𝒃 𝒂 = 𝟗 ∝ 𝜷 = 𝒄 𝒂 = 𝒎 𝜶𝟑 + 𝜷𝟑 = 𝟎 = ∝ +𝜷 𝟑 − 𝟑𝜶𝜷 𝜶 + 𝜷 = 𝟗𝟑 − 𝟑(𝒎) 𝟗 = 𝟗(𝟖𝟏 − 𝟑𝒎) 𝒎 = 𝟐𝟕 𝒎 = 𝟖𝟏 𝟑
- 2. 𝒑𝒈 𝟓𝟗 𝒂 = 𝟐 𝒃 = 𝟕 𝐜 = − 𝟒 ∝ + 𝜷 = − 𝒃 𝒂 = − 𝟕 𝟐 ∝ 𝜷 = 𝒄 𝒂 = − 𝟒 𝟐 = −𝟐 𝒂 𝜶𝟐 + 𝜷𝟐 = ∝ +𝜷 𝟐 − 𝟐𝜶𝜷 = − 𝟕 𝟐 𝟐 − 𝟐 −𝟐 = 𝟒𝟗 𝟒 + 𝟒 = 𝟔𝟓 𝟒
- 3. 𝒑𝒈 𝟓𝟗 𝒂 = 𝟐 𝒃 = 𝟕 𝐜 = − 𝟒 ∝ + 𝜷 = − 𝒃 𝒂 = − 𝟕 𝟐 ∝ 𝜷 = 𝒄 𝒂 = − 𝟒 𝟐 = −𝟐 𝒃 𝜶𝟑 + 𝜷𝟑 = ∝ +𝜷 ∝𝟐 +𝜷𝟐 − 𝜶𝜷 = − 𝟕 𝟐 𝟔𝟓 𝟒 + 𝟐 = − 𝟓𝟏𝟏 𝟖 = 𝟔𝟓 𝟒 𝜶𝟑 + 𝜷𝟑 = ∝ +𝜷 𝟑 − 𝟑𝜶𝜷 𝜶 + 𝜷
- 4. 𝒑𝒈 𝟓𝟗 𝒂 = 𝟐 𝒃 = 𝟕 𝐜 = − 𝟒 ∝ + 𝜷 = − 𝒃 𝒂 = − 𝟕 𝟐 ∝ 𝜷 = 𝒄 𝒂 = − 𝟒 𝟐 = −𝟐 𝒄 𝟏 ∝ + 𝟏 𝜷 = ∝ + 𝜷 𝜶𝜷 = − 𝟕 𝟐 −𝟐 = 𝟕 𝟒 𝒅 ∝ −𝜷 𝟐 = ∝ +𝜷 𝟐 − 𝟒𝜶𝜷 = − 𝟕 𝟐 𝟐 − 𝟒 −𝟐 = 𝟖𝟏 𝟒 ∝ −𝜷 = 𝟗 𝟐 ∝ > 𝜷
- 6. 𝒑𝒈 𝟔𝟎 𝒂 = 𝟏 𝒃 = 𝟏 + 𝟐 𝐜 = 𝟐 ∝ + 𝜷 = − 𝒃 𝒂 = − 𝟏 + 𝟐 ∝ 𝜷 = 𝒄 𝒂 = 𝟐 𝒂 𝜷 ∝ + 𝜶 𝜷 = 𝜶𝟐 + 𝜷𝟐 𝜶𝜷 = ∝ +𝜷 𝟐 − 𝟐𝜶𝜷 𝜶𝜷 = − 𝟏 + 𝟐 𝟐 − 𝟐 𝟐 𝟐 = 𝟑 𝟐 𝟐
- 7. 𝒑𝒈 𝟔𝟎 𝒂 = 𝟏 𝒃 = 𝟏 + 𝟐 𝐜 = 𝟐 ∝ + 𝜷 = − 𝒃 𝒂 = − 𝟏 + 𝟐 ∝ 𝜷 = 𝒄 𝒂 = 𝟐 𝒃 ∝ +𝟏 𝜷 + 𝟏 = ∝ 𝜷 + 𝜶 + 𝜷 + 𝟏 = 𝟐 − 𝟏 + 𝟐 + 𝟏 = 𝟎
- 8. 𝒑𝒈 𝟔𝟎 ∝ + 𝜷 = 𝟑 ∝ 𝜷 = 𝟐 𝒂𝒔𝒔𝒖𝒎𝒆 ∝ = 𝟏 𝜷 = 𝟐 ∴ 𝒙𝟐 − 𝟑𝒙 + 𝟐 = 𝟎
- 9. 𝒑𝒈 𝟔𝟑 𝟑𝒙𝟐 + 𝟒𝒙 − 𝟒 = 𝟎 𝒂 − 𝟐, 𝟐 𝟑 𝒃 𝟏 + 𝟑 𝟐 , 𝟏 − 𝟑 𝟐 𝒄 𝒂, 𝟐𝒂 𝒅 𝒃, 𝟏 𝒃 𝟐𝒙𝟐 − 𝟐𝒙 − 𝟏 = 𝟎 𝒙𝟐 − 𝟑𝒂𝒙 + 𝟐𝒂𝟐 = 𝟎 𝒃𝒙𝟐 − 𝒃𝟐 + 𝟏 𝒙 + 𝒃 = 𝟎 𝒙𝟐 − 𝟑𝒙 − 𝟔 − 𝟐 𝟑 = 𝟎 ∆ > 𝟎 , 𝜶 ≠ 𝜷
- 10. 𝒑𝒈 𝟔𝟏 𝒂 = 𝟑 𝒃 = −𝟒 𝐜 = −𝟓 ∝ + 𝜷 = − 𝒃 𝒂 = 𝟒 𝟑 ∝ 𝜷 = 𝒄 𝒂 = − 𝟓 𝟑 = − 𝟒 𝟑 𝟑 𝟓 ∴ 𝟓𝒙𝟐 + 𝟒𝒙 − 𝟑 = 𝟎 𝟏 ∝ + 𝟏 𝜷 = ∝ + 𝜷 𝜶𝜷 = − 𝟒 𝟓 𝟏 ∝ × 𝟏 𝜷 = − 𝟑 𝟓 𝒙𝟐 + 𝟒 𝟓 𝒙 − 𝟑 𝟓 = 𝟎
- 11. 𝒑𝒈 𝟔𝟒 𝒑𝟐𝒙𝟐 + 𝒑𝒒𝒙 + 𝟐𝟓𝒑𝒓 − 𝟔𝒒𝟐 = 𝟎 𝟔𝒎𝟐 + 𝒏 𝒙𝟐 − 𝟑𝒎𝟐 − 𝟐𝒏 𝒙 + 𝒏 = 𝟎
- 12. 𝒑𝒈 𝟔𝟒 𝒑𝟐𝒙𝟐 + 𝒑𝒒𝒙 + 𝟐𝟓𝒑𝒓 − 𝟔𝒒𝟐 = 𝟎 𝒂 = 𝒑 𝒃 = 𝒒 𝐜 = 𝒓 ∝ + 𝜷 = − 𝒃 𝒂 = − 𝒒 𝒑 ∝ 𝜷 = 𝒄 𝒂 = 𝒓 𝒑 𝟑𝜶 − 𝟐𝜷 + 𝟑𝜷 − 𝟐𝜶 = 𝜶 + 𝜷 = − 𝒒 𝒑 (𝟑𝜶 − 𝟐𝜷)(𝟑𝜷 − 𝟐𝜶) = 𝟗𝜶𝜷 − 𝟔𝜶𝟐 − 𝟔𝜷𝟐 + 𝟒𝜶𝜷 = 𝟏𝟑𝜶𝜷 − 𝟔(𝜶𝟐 + 𝜷𝟐) = 𝟏𝟑𝜶𝜷 − 𝟔 ∝ +𝜷 𝟐 − 𝟐𝜶𝜷 = 𝟐𝟓𝜶𝜷 − 𝟔 ∝ +𝜷 𝟐 = 𝟐𝟓 𝒓 𝒑 − 𝟔 − 𝒒 𝒑 𝟐 ∴ 𝒑𝟐 𝒙𝟐 + 𝒑𝒒𝒙 + 𝟐𝟓𝒑𝒓 − 𝟔𝒒𝟐 = 𝟎
- 13. 𝒑𝒈 𝟔𝟐 ∝ + 𝜷 = − 𝒃 𝒂 ∝ 𝜷 = 𝒄 𝒂 𝟐 + 𝟐 + 𝟐 − 𝟐 = − 𝒃 𝒂 𝟒 = − 𝒃 𝒂 𝒃 = − 𝟒𝒂 𝟐 + 𝟐 𝟐 − 𝟐 = 𝒄 𝒂 𝟐 = 𝒄 𝒂 𝒃 = − 𝟒 𝒄 𝟐 𝒂 = 𝒄 𝟐 ∴ 𝒃 = −𝟐𝒄
- 14. 𝒑𝒈 𝟔𝟑
- 15. 𝒑𝒈 𝟔𝟐, 𝟔𝟑 𝒂 = 𝟏 𝒃 = 𝒑 𝐜 = 𝒒 ∝ + 𝜷 = − 𝒃 𝒂 = − 𝒑 ∝ 𝜷 = 𝒄 𝒂 = 𝒒 𝜶𝟐 − 𝜷𝟐 = − 𝒎 𝜶 + 𝜷 𝜶 − 𝜷 = − 𝒎 −𝒑 𝜶 − 𝜷 = − 𝒎 𝒎 = 𝒑 𝜶 − 𝜷 𝜶𝟐 (−𝜷𝟐) = 𝒏 ∝ −𝜷 𝟐 = ∝ +𝜷 𝟐 − 𝟒𝜶𝜷 = −𝒑 𝟐 − 𝟒𝒒 𝜶 − 𝜷 = 𝒑𝟐 − 𝟒𝒒 ∴ 𝒎 = 𝒑 𝒑𝟐 − 𝟒𝒒 − 𝜶𝜷 𝟐 = 𝒏 − 𝒒 𝟐 = 𝒏 ∴ 𝒏 = − 𝒒𝟐
- 16. 𝒑𝒈 𝟔𝟑, 𝟔𝟒 𝟐𝒙𝟐 − 𝒙 − 𝟑 = 𝟎 𝟑𝒙𝟐 − 𝟏𝟐𝒙 + 𝟏𝟏 = 𝟎 𝒙𝟐 − 𝟏𝟏𝒙 + 𝟐𝟓 = 𝟎 𝒙𝟐 ± 𝟓 𝒙 + 𝟏 = 𝟎
- 17. 𝒑𝒈 𝟔𝟒 𝒂 = 𝟏 𝒃 = 𝟏 𝐜 = −𝟓 ∝ + 𝜷 = − 𝒃 𝒂 = − 𝟏 ∝ 𝜷 = 𝒄 𝒂 = − 𝟓 ∴ 𝒙𝟐 − 𝟏𝟏𝒙 + 𝟐𝟓 = 𝟎 𝜶𝟐 + 𝜷𝟐 = ∝ +𝜷 𝟐 − 𝟐𝜶𝜷 = −𝟏 𝟐 − 𝟐 −𝟓 = 𝟏𝟏 ∝ 𝜷 𝟐 = 𝟐𝟓
- 18. 𝒑𝒈 𝟔𝟑 𝒂 = 𝟑 𝒃 = 𝟔 𝐜 = 𝟐 ∝ + 𝜷 = − 𝒃 𝒂 = −𝟐 ∝ 𝜷 = 𝒄 𝒂 = 𝟐 𝟑 ∴ 𝟑𝒙𝟐 − 𝟏𝟐𝒙 + 𝟏𝟏 = 𝟎 = −𝟐 + 𝟔 = 𝜶𝜷 + 𝟑𝜶 + 𝟑𝜷 + 𝟗 ∝ + 𝟑 + 𝜷 + 𝟑 = 𝜶 + 𝜷 + 𝟔 = 𝟒 = 𝜶𝜷 + 𝟑 𝜶 + 𝜷 + 𝟗 = 𝟐 𝟑 + 𝟑(−𝟐) + 𝟗 (𝜶 + 𝟑)(𝜷 + 𝟑) = 𝟏𝟏 𝟑 𝒙𝟐 − 𝟒𝒙 + 𝟏𝟏 𝟑 = 𝟎
- 19. 𝒑𝒈 𝟔𝟒 ∴ 𝒙𝟐 ± 𝟓 𝒙 + 𝟏 = 𝟎 𝜶𝟐 + 𝜷𝟐 = ∝ +𝜷 𝟐 − 𝟐𝜶𝜷 = 𝟑 − −① ∝ − 𝜷 𝟐 = ∝ +𝜷 𝟐 − 𝟒𝜶𝜷 = 𝟏 − −② ① − ② 𝟐𝜶𝜷 = 𝟐 𝜶𝜷 = 𝟏 𝜶 + 𝜷 = ± 𝟓