ᠯᠠᠪᠯᠠᠬᠤ ᠬᠠᠷᠢᠭᠤᠯᠲᠠ 标准答案.docx

ᠯᠠᠪᠯᠠᠬᠤ ᠬᠠᠷᠢᠭ ᠤᠯᠲᠠ ᠨᠢ᠄ ᠨᠢᠭᠡ ᠭᠠᠭᠴᠠ ᠬᠠᠷ ᠢᠭᠤᠯ ᠲᠠ ᠰᠤᠩᠭᠤᠬ ᠤ ᠰ᠊ ᠡᠲᠤᠪ᠃ 1. A 2. C 3. C 4. D 5. B 6. D 7. A 8. B 9. B 10 .C ᠬᠤᠶ ᠠᠷ ᠬ᠊ ᠣᠭᠤᠰᠤ ᠨ᠊ ᠲᠤ ᠲᠠᠭᠯ ᠠᠬᠤ ᠰᠡ ᠲᠤᠪ᠃ 11 . 1 .05 1 × 10 7 12 . 10 1 3. 2𝜋3 14 . 12 1 5. 2√ 3 16 . ① ② ④ ᠭᠤᠷᠪ ᠠ᠂ ᠪᠣᠳᠣ ᠵᠤ ᠬᠠᠷ ᠢᠭᠤᠯᠬᠤ ᠰᠡ ᠲᠤᠪ᠃ 17. ︵1︶ ᠪᠣᠳᠣ ᠬᠤ ᠨᠢ᠄ ᠲᠡᠩ ᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠨᠢ ᠭᠡ ᠶᠢ ᠪᠣᠳᠣᠪᠠᠯ ᠲᠡ ᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰ ᠤ ᠬᠤᠶ ᠠᠷ ᠢ ᠪᠣᠳᠤᠪᠠᠯ ᠲᠡ ᠩᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠶᠢᠨ ᠪᠦ ᠯᠥᠭ ᠦᠨ ᠬᠠᠷᠢᠭ ᠤ ᠶᠢ ᠨ᠊ ᠴᠤᠭᠯ ᠠᠷᠠᠯ ᠨᠢ ᠲᠡᠩ ᠴᠡᠳᠭᠡᠯ ᠪᠤᠰᠤ ᠶᠢ ᠨ᠊ ᠪᠥᠯᠥ ᠬ᠋᠊ ᠦᠨ ᠬᠠᠮ ᠤᠭ ᠤᠨ ᠪᠠᠭ ᠠ ᠪᠦ ᠬᠥᠯᠢ ᠲᠤᠭ ᠠᠨ ᠤ ᠬᠠᠷ ᠢᠭᠤ ᠨᠢ ᠤ ᠣᠯᠣᠨ ᠠ᠃ ︵2︶ ᠪᠣᠳᠣ ᠬᠤ ᠨᠢ᠄ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠢ ᠣᠯᠬ ᠤ ᠠ ᠷᠭ ᠠ ᠨᠢᠭᠡ᠄ ᠬᠡᠮᠵᠢᠭ ᠳᠡᠯ ᠢ ᠣᠯᠬ ᠤ ᠠ ᠷᠭ ᠠ ᠬᠤᠶ ᠠᠷ᠄ 18 . ︵ᠲᠤᠰ ᠪᠠ ᠬ᠋᠊ ᠠ ᠰᠡᠳᠦᠪ ᠨᠡᠢᠲᠡ 9 ᠬᠤᠪᠢ︶ ︵1︶ 𝑎= ︵7︶᠂ ᠳᠤᠮᠳᠠ ᠪᠠ ᠢᠷᠢ ᠶᠢᠨ ᠲᠤᠭ ᠠ ᠨᠢ ︵2 .5︶ ᠴᠠᠭ ︵2︶ ᠲᠤ ᠤ ᠥᠨᠴ ᠦᠭ ᠦ ᠨ᠊ ᠭᠷ ᠠᠳᠦ᠋ᠰ ᠤᠨ ᠲᠤᠭ ᠠ ᠨᠢ ︵7 2︶ ᠭᠷᠠᠳᠦ᠋ᠰ ︵3︶ ᠪᠤᠳᠤ ᠬᠤ ᠨᠢ᠄ ︵50 − 20︶ × 20% = 6 600 × 6: 6 50 = 144 ︵ᠰᠤᠷᠤᠭᠴᠢ︶ ᠬᠠᠷᠢᠭ ᠤ᠄ ᠨᠢᠭᠡ ᠭᠠᠷᠠᠭ ᠤᠨ ᠳᠠᠪᠲᠠ ᠯᠭ ᠠ ᠬᠢᠭᠰ ᠠ ᠴᠠ ᠬ᠋᠊ ᠨᠢ 4 ᠴᠠᠭ ᠪᠤᠯᠠᠬᠤ ᠰᠤᠷᠤᠭᠴᠢ ᠪᠠᠷᠤᠭ 14 4 ᠪᠠᠢᠨ ᠠ᠃ ︵4︶ ᠪᠤᠳᠤ ᠬᠤ ᠨᠢ᠄ ∵ ᠨᠡ ᠢᠲᠡ 12 ᠵ᠊ ᠦᠢᠯ ᠦ ᠨ᠊ ᠤ ᠤᠯᠤᠯᠴᠠ ᠭᠠᠲᠤ ᠦᠷ ᠡ ᠳ᠋᠊ ᠦᠩ ᠲᠠ ᠢ᠂ ᠡᠭᠦᠨ ᠲᠤ ᠶᠠᠭ ᠰᠠᠢᠬᠠᠨ ᠤᠯᠠᠭ ᠠᠨ ᠤ ᠠ ᠵᠢᠮ ᠢᠰ ᠤ ᠣᠯᠬᠤ ᠶᠢ ᠨ᠊ ᠦᠷ ᠡ ᠳᠦ᠋ ᠩ᠊ ᠨᠢ 2 ᠵᠦᠯ ᠪᠠᠢᠨ ᠠ᠃ ∴ P ︵ᠤᠯ ᠠᠭᠠᠨ ᠪᠠ ᠵᠢᠮ ᠢᠰ ᠢ ᠰᠤᠩᠭᠤᠬ ᠤ︶ = 212 = 16 ︵ᠲᠣᠳᠣᠷ ᠬᠠᠢᠯᠠᠬ ᠤ ᠨᠢ᠄ 1. ᠮ᠊ ᠤᠳᠤᠯᠵᠢᠨ ᠵᠢᠷ ᠤᠭ ᠤᠨ ︽ᠡᠬ ᠢᠯᠡᠬᠦ︾ ᠭᠡᠳᠡ ᠬ᠋᠊ ᠦᠭᠡ ᠶᠢ ᠪᠢᠴᠢᠬᠦ ᠦᠭᠡᠢ ᠪᠠᠢᠭᠰᠠᠨ ᠴᠦ ᠬᠤᠪᠢ ᠬᠠᠰ ᠤᠬᠤ ᠦᠭᠡᠢ᠃ 2. ︽ᠨᠡᠢᠲᠡ 12 ᠵᠦᠯ ᠦᠨ ᠪᠤᠯᠤᠯ ᠴᠠᠭᠠᠲᠤ ᠦᠷ ᠡ ᠳ᠋᠊ ᠦᠩ ᠲᠠᠢ᠂ ᠲᠡᠭᠦᠨ ᠲᠤ ᠶ᠊ ᠠᠭ ᠰᠠᠢ ᠬᠠᠨ ᠤᠯᠠᠭ ᠠᠨ ᠪᠠ ᠵᠢᠮᠢᠰ ᠪᠣᠯᠬ ᠤ ᠶᠢ ᠨ᠊ ᠦᠷ ᠡ ᠳᠦ᠋ᠩ ᠨᠢ 2 ᠵᠦ᠋ ᠢᠯ ᠪᠠᠢᠨ ᠠ︾ ᠤ ᠣᠯᠤᠨ ᠤ ᠯᠠᠭᠠᠨ ᠣ ᠶᠣᠨ ᠨᠣᠮ ᠶᠢᠨ ᠵᠢᠮ ᠢᠰ ᠣ ᠶᠣᠨ ᠤ ᠯᠠᠭᠠᠨ ᠨᠣᠮ ᠶᠢᠨ ᠵᠢᠮ ᠢᠰ ᠤ ᠯᠠᠭᠠᠨ ᠨᠣᠮ ᠶᠢᠨ ᠤᠯᠠᠭ ᠠᠨ ᠵᠢᠮ ᠢᠰ ᠣ ᠶᠣᠨ ᠵᠢᠮ ᠢᠰ ᠤᠯ ᠠᠭᠠᠨ ᠨᠣᠮ ᠶᠢᠨ ᠡᠬᠢᠯ ᠡᠬᠦ ᠤᠶᠤᠨ ᠤᠯᠠᠭ ᠠᠨ ᠨᠣᠮᠢᠨ ᠵᠢᠮᠢᠰ ᠤᠶᠤᠨ ᠤᠶᠤ ᠨ᠊ ᠤᠯᠠᠭ ᠠᠨ ᠤᠶᠤᠨ ᠨᠣᠮᠢᠨ ᠤᠶᠤᠨ ᠵᠢᠮᠢᠰ ᠤᠯ ᠠᠭᠠᠨ ᠤᠯᠠᠭ ᠠᠨ ᠤᠶᠤᠨ ᠤᠯ ᠠᠭᠠᠨ ᠨᠣᠮᠢᠨ ᠤᠯᠠᠭ ᠠᠨ ᠵᠢᠮᠢᠰ ᠨᠣᠮ ᠶᠢᠨ ᠨᠣᠮᠢᠨ ᠤᠶᠤᠨ ᠨᠣᠮᠢᠨ ᠤᠯᠠᠭ ᠠᠨ ᠨᠣᠮᠢᠨ ᠵᠢᠮᠢᠰ ᠵᠢᠮ ᠢᠰ ᠵᠢᠮᠢᠰ ᠤᠶᠤᠨ ᠵᠢᠮᠢᠰ ᠤᠯᠠᠭ ᠠᠨ ᠵᠢᠮᠢᠰ ᠨᠣᠮᠢᠨ ︽ᠢᠯ ᠡᠷᠬᠡᠢᠯ ᠡᠯ 212︾ ᠦᠨ ᠨᠢᠭᠡ ᠶᠢ ᠨᠢ ᠤ ᠢᠴᠢᠪᠡ ᠯ᠊ ᠳᠠᠷ ᠤᠢ ᠬᠤᠪᠢ ᠤᠯ ᠭᠤᠨ ᠠ᠃︶ 19. ︵ᠲᠣᠰ ᠪᠠ ᠬ᠋᠊ ᠠ ᠰᠡᠳᠦᠪ ᠨᠡᠢᠲᠡ 8 ᠬᠤᠪᠢ︶ ᠪᠤᠳᠤᠬ ᠤ ᠨᠢ᠄ ︵1︶ ᠴᠡᠭ A ︵4,3︶ ᠢ y= 𝑎𝑥 ᠲᠤ ᠣᠷᠤᠯ ᠠᠭᠤᠯ ᠪᠠᠯ 3= 𝑎4 ∴a = 12 ∵OA = OB ᠪᠦᠭᠡᠳ ᠴᠡ ᠬ᠋᠊ B ᠨᠢ y ᠲᠡ ᠩᠭᠡᠯ ᠢᠭ ᠦ ᠨ᠊ ᠰᠤᠬ ᠡᠷᠬᠦ ᠬᠠᠭ ᠠᠰ ᠲᠡᠩᠭᠡᠯ ᠢᠭ ᠳᠡᠭᠡᠷ ᠡ ᠤᠷ ᠤᠰᠢᠨ ᠠ ∴B ︵0 ,− 5︶ ᠴᠡᠭ A ︵4 ,3︶ ,B ︵0 ,− 5︶ ᠢ ᠲᠤᠰ ᠲᠤᠰ 𝑦= 𝑘𝑥 + 𝑏 ᠲᠤ ᠣᠷᠤ ᠯᠠᠭᠤᠯ ᠪᠠᠯ᠄ { 4 𝑘+ 𝑏= 3 𝑏= −5 ᠪᠤᠳᠤᠭᠠ ᠳ᠋᠊ ᠣ ᠯᠬᠤ ᠨᠢ { 𝑘 = 2 𝑏= −5 ∴ ᠹᠦᠩᠺᠼ ᠦ ᠨ᠊ ᠠ ᠨᠠᠯᠢᠰ ᠢᠯ ᠡᠷᠬᠡᠢᠯ ᠡᠯ ᠨ᠊ ᠢ 𝑦 = 2𝑥 − 5 ᠪᠠ y = 12𝑥 ᠪᠤᠯ ᠤᠨ ᠠ ︵2︶ ∵ MB = MC ,B ︵0 ,− 5︶ ,𝐶 ︵0 ,5︶ ∴ ᠴᠡᠭ M ᠨᠢ ᠬᠡ ᠷᠴᠢᠮ BC ᠶᠢᠨ ᠡᠭᠴᠡ ᠲᠠ ᠯᠠᠯᠠᠨ ᠬᠤᠪᠢᠶ ᠠᠭᠴᠢ ᠲᠡᠭᠡᠷ ᠡ ᠤᠷᠤᠰ ᠶᠢᠨ ᠠ᠂ 𝑥 ᠲᠡᠩᠭᠡᠯ ᠢᠭ ᠳᠡ ᠭᠡᠷ ᠡ ᠪᠤᠢ ᠪᠠᠰᠠ ∵ ᠴᠡᠭ M ᠨᠢ ᠨᠢᠭᠡᠳᠦᠭᠡᠷ ᠵᠡᠷ ᠭᠡ ᠶᠢᠨ ᠹᠦᠩᠺᠼ 𝑦 = 2𝑥 − 5 ᠦ ᠨ᠊ ᠵᠢᠷ ᠤᠭ ᠳᠡᠭᠡᠷ ᠡ ᠣᠷᠣᠰ ᠶᠢᠨ ᠠ ∴ ᠴᠡᠭ M ᠨᠢ ᠰᠢᠯᠤᠭᠤᠨ 𝑦= 2𝑥 − 5 ᠪᠣᠯᠣᠨ 𝑥 ᠲᠡᠩᠭᠡᠯ ᠢᠭ ᠦ ᠨ᠊ ᠤ ᠭᠲᠤᠯ ᠤᠯᠴᠠᠯ ᠤ ᠨ᠊ ᠴᠡ ᠬ᠋᠊ ᠪᠤᠯᠤᠨ ᠠ 2 𝑥− 5= 0 ᠢ ᠪᠤᠳᠤᠭᠠ ᠳ᠋᠊ ᠣ ᠯᠬᠤ ᠨᠢ 𝑥 = 52 ∴ ᠠ ᠡ ᠦᠶ ᠡᠰ ᠦ ᠨ᠊ ᠴᠡ ᠬ᠋᠊ M ᠦ ᠨ᠊ ᠤ ᠠᠢᠷᠢᠰᠢᠯ ᠨᠢ ︵52 ,0︶ 20. ︵ᠲᠤᠰ ᠰᠡ ᠳᠦᠪ ᠨᠡᠢᠲᠡ 8 ᠬᠤᠪᠢ︶ ᠪᠤᠳᠤᠬ ᠤ ᠨᠢ᠄ ᠪᠤᠳᠤᠬ ᠤ ᠠ ᠷᠭ ᠠ 1᠄ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ᠂ ᠴᠡᠭ A ,B ᠶᠢ ᠳᠠᠭ ᠠᠷᠢᠭ ᠤᠯᠤᠨ AD ⊥ OC , BE ⊥ OC ᠪᠠᠷ ᠪᠠᠢᠭ ᠤᠯᠤᠨ ᠠ᠂ ᠡᠭᠴᠡ ᠶᠢᠨ ᠰᠠᠭ ᠤᠷᠢ ᠨᠢ ᠲᠣᠰ ᠲᠣᠰ ᠴᠡᠭ D ᠪᠠ E᠂ ᠪᠠᠰᠠ ᠴᠡᠭ A ᠶᠢ ᠳᠠᠭ ᠠᠷᠢᠭ ᠤᠯᠤᠨ AE ⊥ EB ᠪᠠᠷ ᠪᠠᠢᠭ ᠤᠯᠤᠨ ᠠ᠂ ᠡᠭᠴᠡ ᠶᠢᠨ ᠰᠠᠭ ᠤᠷᠢ ᠨᠢ ᠴᠡ ᠬ᠋᠊ F᠂ ᠲᠡ ᠭᠡᠪᠡᠯ ᠳᠦ᠋ᠷᠪ ᠡᠯᠵᠢᠨ ADE F ᠨᠢ ᠲᠡᠭᠰᠢ ᠦᠨᠴ ᠦᠭᠲᠦ ᠪᠤᠯᠤᠨ ᠠ᠃ ∴∠ DAF = 90° ,DE = AF RT △ OAD ᠲᠤ᠂ ∠A OC = 26° ,OA = 10 ∴OD = OA ∙c os ∠A OC ≈ 10 × 0.90 F E D B A O C RT △ FAB ᠲᠤ ,∠ FAB = 60° ,AB = 8 ∴AF = AB · c os ∠F AB = 8 × 12 = 4 ∴DE = AF = 4 ∵ ᠰ᠊ ᠦᠷᠴᠢᠭ ᠦᠷ ᠦ ᠨ᠊ ᠬᠠᠮᠤᠭ ᠳᠡ ᠭᠡᠳᠦ ᠴᠡ ᠬ᠋᠊ B ᠪᠠ ᠭᠠᠵᠠᠷ ᠤᠨ ᠨᠢᠭᠤᠷ ᠤᠨ ᠬ᠊ ᠤᠭᠤᠷᠤᠨᠳ ᠤᠬᠢ ᠵᠠᠢ ᠨᠢ 175 + 15 = 190 ︵cm︶ ∴ ᠴᠡᠭ O ᠪᠠ ᠭᠠᠵᠠᠷ ᠤᠨ ᠨᠢᠭᠤᠷ ᠤᠨ ᠬᠤᠭᠤᠷ ᠤᠨᠳᠤᠬ ᠢ ᠵᠠᠢ ᠨᠢ 190 − 9− 4= 177 ︵cm︶ ᠬᠠᠷᠢᠭ ᠤ᠄ ᠴᠡ ᠬ᠋᠊ O ᠪᠠ ᠭᠠᠵᠠᠷ ᠤᠨ ᠨᠢᠭ ᠤᠷ ᠠᠴᠠ 17 7cm ᠵᠶᠢᠲᠠᠢ ᠪᠠᠢᠪ ᠠᠯ ᠵ᠊ ᠤᠬᠢᠨ ᠠ᠃ ᠪᠤᠳᠤᠬ ᠤ ᠠ ᠷᠭ ᠠ 2᠄ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ᠂ ᠬᠠᠨ ᠠ CO ᠶᠢᠨ ᠳᠤᠲᠤᠷ ᠠ ᠦᠵ ᠦᠭᠦᠷ ᠦ ᠨ᠊ ᠴᠡ ᠬ᠋᠊ ᠢ M ᠭᠡᠵᠦ᠂ MN ⊥ CM ᠪᠠᠷ ᠪᠠᠢᠭ ᠤᠯᠤᠨ ᠠ᠂ ᠪᠠᠰᠠ ᠴᠡ ᠬ᠋᠊ A , B ᠶᠢ ᠳᠠᠭ ᠠᠷᠢᠭ ᠤᠯᠤᠨ AD ⊥ MN ,BE ⊥ MN ᠪᠠᠷ ᠪᠠᠢᠭ ᠤᠯᠤᠨ ᠠ᠂ ᠡᠭ ᠴᠡ ᠶᠢᠨ ᠰᠠᠭ ᠤᠷᠢ ᠨᠢ ᠲᠣᠰ ᠲᠣᠰ ᠴᠡᠭ D ᠪᠠ E᠃ AQ ⊥ BE ,OF ⊥ AD ᠪᠠᠷ ᠪᠠᠢᠭ ᠤᠯᠤᠨ ᠠ᠂ ᠡᠭᠴᠡ ᠶᠢᠨ ᠰᠠᠭ ᠤᠷᠢ ᠨᠢ ᠲᠣᠰ ᠲᠣᠰ ᠴᠡᠭ Q ᠤ ᠠ F ᠪᠣᠯ ᠣᠨ ᠠ᠃ ADE Q ∴∠ DA Q = 90° ∵MN ⊥ CM ,AD ⊥ MN ∴CM ∕∕ AD ∴ ∠O AF = ∠A OC = 26 ° Rt △ AO F ∠O AF = 26 °, OA = 10 ∴AF = OA ∙c os ∠O AF ≈ 10 × 0.90 = 9 ∵∠ BA Q = ∠O AB − ∠O AF − ∠D AQ = 146° − 26° − 90° = 30° Rt △ AB Q ∠B AQ = 30 ° , AB = 8 ∴BQ = 12 AB = 12 × 8= 4 ∵ B BE = 175 + 15 = 190 ︵cm︶ ∴OM = BE − BQ − AF = 190 − 4− 9= 177 ︵cm︶ O 17 7c m A MN ⊥ OC ,BN ⊥ MN M Q ED F B A O C M N M N B A O C N ∵Rt △ OAM ∠C OA = 26° ,OA = 10 ∴∠ OAM = 90° − 26° = 64° OM = OA ∙c os ∠C OA ≈ 10 × 0.90 = 9 ∵∠ OAB = 146° ∴∠ BAN = 146° − ︵18 0° − 64°︶ = 30° AB = 8 , BN ⊥ MN ∴BN = 12 AB = 12 × 8= 4 ∵ B 17 5+ 15 =1 90 ︵cm︶ ∴ 190 − 9− 4= 177 ︵cm︶ O 17 7c m 21. ︵︶ ︵1︶ ︵𝑥 + 3︶ 2+ ︵𝑦 + 1︶ 2= 3 ︵2︶ ① ∵BC = BD ,BD ⊥ OC ∴∠ CB E= ∠O BE ∵BE = BE ,BC = BO ∴△ CB E≌ △ OB E ︵SA S︶ ∴∠ BC E= ∠B OE ∵ ☉B y O ∴∠ BO E= 90 ° ∴∠ BC E= ∠B OE = 90° ∴EC ⊥ BC ∵BC ☉ ∴EC ☉ ② ∵∠ECB = ∠EO B= 90° ∴QB = QC = QO = 12 𝐵𝐸 x y A D E B O C x y Q A D E B O C ∵BD ⊥ OC ∴∠ BD O = 90 ° ∴∠ OB E+ ∠A OC = 90 ° ∵ EO B= 90 ° ∴∠ OB E+ ∠B EO = 90 ° ∴∠ AO C= ∠B EO ∵sin ∠A OC = 35 ∴sin ∠B EO = 35 Rt △ BO E sin ∠B EO = OBBE ∴ OBBE = 35 ∵B ︵− 3,0︶ ∴OB = 3 ∴BE = 5 ∴QB = 12 𝐵𝐸 = 52 OE = 4 ∴E ︵0 ,4︶ ∵Q ∴Q ︵− 32 , 2︶ ∴ Q QB ☉Q ︵𝑥 + 32︶ 2+ ︵𝑦 − 2︶ 2= 254 ︵2︶ ① ∵ ☉B ∴∠ BO E= 90° ∵BD ⊥ OC ∴BE OC ∵EO = EC ∴∠ EO C= ∠EC O ∵BO = BC ∴∠ BO C= ∠B CO ∴∠ EO C+ ∠B OC = ∠EC O+ ∠B CO ∴∠ BC E= ∠B OE = 90 ° ∴BC ⊥ EC ∵BC ☉ x y A D E B O C ∴EC ☉ ② ∵∠ BO E= ∠B CE = 90 ° ∴ C O BE ∴ Q BE QB = QC = QO = QE = 12 𝐵𝐸 ∵ B ︵− 3 , 0︶ ∴OB = 3 ∵∠ BO E= 90° , BD ⊥ OC ∴∠ AO C+ ∠DOE = 90° , ∠ DOE + ∠B EO = 90° ∴∠ AO C= ∠B EO ∴sin ∠A OC = sin ∠B EO = 35 Rt △ BO E sin BEO = OBBE ∴ OBBE = 35 ∴BE = 5 ∴QB = 12 BE = 52 OE = √BE 2− OB 2= 4 ∴ E ︵0 ,4︶ ∴ BE Q ︵− 32 , 2︶ ∴ Q QB ☉Q ︵𝑥 + 32︶ 2+ ︵𝑦 − 2︶ 2= 254 22. ︵︶ ︵1︶ m 10 ︵1 − 𝑚︶ 2= 8.1 𝑚 1= 0.1 = 10 % ,𝑚 2= 1.9 ∴m = 10 % 10 % ︵2︶ x y Q A D E B O C y= ︵8 .1 − 4.1︶ ︵1 20 − 𝑥︶ − ︵3 𝑥 2 − 64 𝑥+ 400︶ = 480 − 4𝑥 − 3𝑥 2+ 64 𝑥− 400 ∴𝑦 = −3 𝑥 2 + 60 𝑥+ 80 ︵1 ≤ 𝑥 10︶ ∴y = −3 ︵𝑥 2− 20 𝑥︶ + 80 = −3 ︵𝑥 − 10︶ 2 + 380 ∵a = −3 0 ∴x 10 ∵1 ≤ 𝑥 10 ∴x = 9 𝑦= −3 ︵9 − 10︶ 2 + 380 = 377 𝑦= −3 𝑥 2 + 60 𝑥+ 80 ︵1 ≤ 𝑥 10︶ y= ︵8 .1 − 4.1︶ ︵1 20 − 𝑥︶ − ︵3 𝑥 2 − 64 𝑥+ 400︶ = 480 − 4𝑥 − 3𝑥 2+ 64 𝑥− 400 = 480 − 4x − 3𝑥 2+ 60 𝑥+ 80 ︵1 ≤ 𝑥 10︶ ∵x = − 𝑏2𝑎 = 10 , 𝑎= −3 0 ∴x 10 x ∵1 ≤ 𝑥 10 x ∴x = 9 y= −3 × 9 2 + 60 × 9+ 80 = 377 y x 𝑦= −3 𝑥 2 + 60 𝑥+ 80 ︵1 ≤ 𝑥 10︶ 23. ︵ᠲᠣᠰ ᠪᠠᠭ ᠠ ᠰ᠊ ᠡᠲᠥᠪ ᠨᠡᠢᠲᠡ 10 ᠬᠤᠪᠢ︶ ︵1︶ 【 ᠤᠷ ᠤᠯᠳᠤ ᠯᠭ ᠠ ᠠᠴ ᠠ ᠠ ᠵᠢᠭᠯ ᠠᠵᠤ ᠣ ᠯᠬᠤ 】 ᠪᠤᠳᠤᠬ ᠤ ᠨᠢ᠄ ① ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ ② ∠AB ′B = 45° ︵2︶ 【 ᠠᠰᠠᠭᠤᠳᠠ ᠯ᠊ ᠢ ᠰᠢᠢᠳ ᠪᠦᠷᠢᠯᠠᠬ ᠦ 】 ᠪᠤᠳᠤᠬ ᠤ ᠨᠢ᠄ ᠪᠤᠳᠤᠬ ᠤ ᠠ ᠷᠭ ᠠ 1᠄ ᠴᠡᠭ E ᠶᠢ ᠳᠠᠭ ᠠᠷᠢᠭ ᠤᠯᠤᠨ EF ⊥ CD ᠪᠠᠷ ᠪᠠᠢᠭ ᠤᠯᠪᠠ ᠯ᠊ CD ᠤᠨ ᠦᠷᠭᠦᠯ ᠵᠢᠯᠡᠯ ᠦᠨ ᠱᠤᠭᠤᠮ ᠲᠠᠢ ᠴᠡᠭ F ᠲᠤ ᠤᠭ ᠲᠤᠯᠤᠯ ᠴᠠᠨ ᠠ᠂ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ ᠲᠡᠭᠡᠪ ᠡᠯ ∠ EF A= 90° ∵ ∠ C= 90° ∴ ∠B + ∠B AC = 90 °,∠C = ∠EF A ∵ AB ᠶᠢ ᠴᠡᠭ A ᠪᠠ ᠷ᠊ ᠲᠥᠪ ᠪᠤ ᠯᠭᠠᠨ ᠴᠠᠭ ᠤᠨ ᠵᠡᠭᠦᠦ ᠶᠢᠨ ᠳᠠ ᠭᠠᠤ ᠴᠢᠭᠯᠡᠯ 90° ᠡᠷᠭᠢᠭ ᠦᠯᠪᠡ ᠯ᠊ AE ᠶᠢ ᠣᠯᠤᠨ ᠠ ∴ ∠ BAE = 90° ,AB = AE ∴ ∠B AC + ∠E AF = 90 ° ∴ ∠B = ∠E AF ︵ᠡᠰᠠᠬ ᠦᠯ ᠡ ∠B AC = ∠AEF ᠪᠠᠷ ᠪᠠᠲᠤᠯ ᠠᠵᠤ ᠪᠣᠯᠤᠨ ᠠ︶ ∴ ∆ AB C≅ ∆E AF ∴ BC = AF ,AC = EF ∵ BC = CD = 1 ∴ AF = CD ∴ AF − AD = CD − AD ᠳᠠᠷ ᠦᠢ᠄ AC = DF ∵ AC = EF ∴ EF = DF ∴ ∆ DEF ᠪᠣᠯ ᠠᠳᠠᠯᠢ ᠬᠠᠵᠠᠭᠤᠲᠤ ᠲᠡᠭ ᠰᠢ ᠦᠨᠴ ᠦᠭᠲᠦ ᠭᠤᠷᠪ ᠠᠯᠵᠢ ᠨ᠊ ∴ ∠ ED F= 45° ∵ ∠ ED F+ ∠ADE = 180 ° ∴ ∠ADE = 180 °− ∠E DF = 180 °− 45° = 135° ᠪᠤᠳᠤᠬ ᠤ ᠠ ᠷᠭ ᠠ 2᠄ ᠵᠢᠷ ᠤᠭ ᠮᠡᠲᠦ᠂ CD ᠳᠡᠭᠡᠷ ᠡ ᠠᠴᠠ CM = CA ᠪᠠᠷ ᠤᠭᠲᠤᠯ ᠤᠨ ᠠᠪᠴᠤ᠂ AM ᠶᠢ ᠬ᠊ ᠣᠯᠪᠤᠨ ᠠ ∵ ∠ C= 90° ∴ ∆CAM ᠪᠣᠯ ᠠᠳᠠᠯᠢ ᠬᠠ ᠵᠠᠭᠤᠲᠤ ᠲᠡᠭᠰᠢ ᠦᠨᠴ ᠦᠭᠲᠦ ᠭᠤᠷᠪ ᠠᠯᠵᠢᠨ ∴ ∠ AMC = 45° A B' C'' BC D F E B AC D E C A B M ∴ ∠AMB = 180 °− ∠AMC = 180 °− 45° = 13 5° ∵ BC = CD = 1, CM = CA ∴ BC − CM = CD − CA ᠳᠠᠷᠦ ᠢ᠄ BM = AD ∵ ∠ C= 90° ∴ ∠B + ∠B AC = 90 ° ∵ AB ᠶᠢ ᠴᠡᠭ A ᠪᠠ ᠷ᠊ ᠲᠥᠪ ᠪᠣᠯ ᠭᠠᠨ ᠴᠠ ᠬ᠋᠊ ᠤᠨ ᠵᠡ ᠭᠦᠦ ᠶᠢᠨ ᠳᠠ ᠭᠠᠤ ᠴᠢᠭᠯᠡᠯ 90° ᠡᠷᠭᠢᠭ ᠦᠯᠪᠡ ᠯ᠊ AE ᠶᠢ ᠣᠯᠤ ᠨ᠊ ᠠ᠃ ∴ ∠ BAE = 90° ,AB = AE ∴ ∠B AC + ∠E AD = 90 ° ∴ ∠B = ∠E AD ∴ ∆ BM A≅ ∆ADE ︵S AS︶ ∴ ∠ADE = ∠AMB = 135° ︵3︶ 【 ᠦᠷᠭᠡᠳᠬ ᠠ ᠬᠡ ᠷᠡᠭᠯᠠᠬ ᠦ 】 ᠪᠤᠳᠤᠬ ᠤ ᠨᠢ᠄ ᠪᠤᠳᠤᠬ ᠤ ᠠ ᠷᠭ ᠠ 1᠄ AC ᠶᠢ ᠬ᠊ ᠣᠯᠪᠤᠨ ᠠ ∵ BE = CE ,AE ⊥ BC ∴ AB = AC ,BC = 2B E= 2 ∆AB D ᠶᠢ ᠴᠡᠭ A ᠪᠠᠷ ᠲᠥᠪ ᠪᠣᠯᠭ ᠠᠨ ᠴᠠᠭ ᠤ ᠨ᠊ ᠵᠡᠭᠦᠦ ᠶᠢᠨ ᠡᠰᠡᠷ ᠭᠦ ᠴᠢᠭᠯᠡᠯ ᠢᠶᠡᠷ ∠B AC ᠦᠨ ᠭᠷ ᠠᠳᠥᠰ ᠤ ᠨ᠊ ᠲᠤᠭ ᠠ ᠪᠠᠷ ᠡᠷ ᠭᠢᠭᠦᠯ ᠪᠡᠯ ∆ ACH ᠶᠢ ᠣᠯᠤᠨ ᠠ᠂ CH ᠶᠢ ᠬᠤᠯ ᠪᠤᠨ ᠠ᠃ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ ᠲᠡᠭᠡᠪ ᠡᠯ ∠B AC = ∠D AH ,AD = AH ,BD = CH ∴ ABAD = 𝐴𝐶𝐴𝐻 ∴ ∆ AB C∽ ∆ADH ∴ BCDH = 𝐴𝐵𝐴𝐷 ,∠AB C= ∠ADH ∵ AD = 𝑘AB ∴ DH = 𝑘BC = 2𝑘 ∵ AE ⊥ BC ∴ ∠B AE + ∠AB C= 90 ° ∵ ∠B AE = ∠ADC ∴ ∠ADC + ∠ADH = 90 ° ᠳᠠᠷᠦ ᠢ᠄ ∠ CDH = 90° Rt ∆C DH ᠲᠤ᠂ ᠬ᠊ ᠤᠶᠠᠷ ᠡᠭᠴᠡ ᠲᠠᠯ ᠠ ᠶᠢᠨ ᠪᠠᠲᠤᠶ ᠤᠰᠤ ᠤ ᠠᠷ ᠤ ᠤᠳᠤᠭᠠ ᠳ᠋᠊ ᠣ ᠯᠬᠤ ᠨᠢ᠄ CH = √𝐶𝐷 2+ 𝐷𝐻 2= √ ︵2𝑘︶ 2 + 3 2 = √4 𝑘 2 + 9 ∴ BD = CH = √4 𝑘 2 + 9 H E A B D C ᠪᠤᠳᠤᠬ ᠤ ᠠ ᠷᠭ ᠠ 2᠄ AC ᠶᠢ ᠬᠤᠯᠪᠤᠨ ᠠ᠂ AD ᠶᠢ ᠴᠡᠭ A ᠪᠠ ᠷ᠊ ᠲᠥᠪ ᠪᠣᠯ ᠭᠠᠨ ᠴᠠ ᠬ᠋᠊ ᠤᠨ ᠵᠡᠭᠦᠦ ᠶᠢᠨ ᠡᠰᠡᠷ ᠭᠦ ᠴᠢᠭᠯᠡᠯ ᠢᠶᠡᠷ ∠B AC ᠦᠨ ᠭᠷᠠᠳᠥᠰ ᠤᠨ ᠲᠤᠭ ᠠ ᠪᠠᠷ ᠡᠷᠭᠢᠭ ᠦᠯᠪᠡ ᠯ᠊ AH ᠶᠢ ᠣᠯᠤ ᠨ᠊ ᠠ᠂ CH ᠶᠢ ᠬᠤ ᠯᠪᠤᠨ ᠠ᠃ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ ᠲᠡᠭᠡᠪ ᠡᠯ ∠B AC = ∠D AH ,AD = AH ∴ ∠B AC + ∠CAD = ∠D AH + ∠CAD ᠳᠠᠷᠦ ᠢ᠄ ∠ BAD = ∠CA H ∵ BE = CE = 1, AE ⊥ BC ∴ AB = AC ,BC = 2B E= 2 ∴ ∆ AB D ∽ ∆A CH ︵SA S︶ ∴ BD = CH ∵ ∠B AC = ∠D AH ,AB = AC ,AD = AH ∴ ∆ AB C∽ ∆ADH ∴ BCDH = 𝐴𝐵𝐴𝐷 ,∠AB C= ∠ADH ∵ AD = 𝑘AB ∴ DH = 𝑘BC = 2𝑘 ∵ AE ⊥ BC ∴ ∠B AE + ∠AB C= 90 ° ∵ ∠B AE = ∠ADC ∴ ∠ADC + ∠ADH = 90 ° ᠳᠠᠷᠦ ᠢ᠄ ∠ CDH = 90° Rt ∆CDH ᠲᠤ᠂ ᠬ᠊ ᠤᠶᠠᠷ ᠡᠭᠴᠡ ᠲᠠᠯ ᠠ ᠶᠢᠨ ᠪᠠᠲᠤᠶ ᠤᠰᠤ ᠤ ᠠᠷ ᠤ ᠤᠳᠤᠭᠠ ᠳ᠋᠊ ᠣ ᠯᠬᠤ ᠨᠢ᠄ CH = √𝐶𝐷 2+ 𝐷𝐻 2= √ ︵2𝑘︶ 2 + 3 2 = √4 𝑘 2 + 9 ∴ BD = CH = √4 𝑘 2 + 9 ᠪᠤᠳᠤᠬ ᠤ ᠠ ᠷᠭ ᠠ 3᠄ AC ᠶᠢ ᠬ᠊ ᠣᠯᠪᠤᠨ ᠠ ∵ BE = CE = 1, AE ⊥ BC ∴ AB = AC ,BC = 2B E= 2 ∴ ∠AB C= ∠A CB ∴ ∠AB C= 12 ︵18 0° − ∠B AC︶ ∆AB D ᠶᠢ ᠴᠡᠭ A ᠪᠠᠷ ᠲᠥᠪ ᠪᠣᠯᠭ ᠠᠨ ᠴᠠᠭ ᠤ ᠨ᠊ ᠵᠡᠭᠦᠦ ᠶᠢᠨ ᠡᠰᠡᠷ ᠭᠦ ᠴᠢᠭᠯᠡᠯ ᠢᠶᠡᠷ ∠B AC ᠦᠨ ᠭᠷ ᠠᠳᠥᠰ ᠤᠨ ᠲᠤᠭ ᠠ ᠪᠠᠷ ᠡᠷ ᠭᠢᠭᠦᠯ ᠪᠡᠯ ∆ ACH ᠶᠢ ᠣᠯᠤᠨ ᠠ᠂ HD ᠶᠢ ᠬᠤᠯ ᠪᠤᠨ ᠠ᠃ ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ H E A B D C ᠲᠡᠭᠡᠪ ᠡᠯ ∠B AC = ∠D AH ,AD = AH ∴ ∠ADH = ∠AHD ∴ ∠ADH = 12 ︵180 °− ∠D AH︶ ∴ ∠AB C= ∠ADH ∴ ∆ AB C∽ ∆ADH ∴ BCDH = 𝐴𝐵𝐴𝐷 ,∠AB C= ∠ADH ∵ AD = 𝑘AB ∴ DH = 𝑘BC = 2𝑘 ∵ AE ⊥ BC ∴ ∠B AE + ∠AB C= 90 ° ∵ ∠B AE = ∠ADC ∴ ∠ADC + ∠ADH = 90 ° ᠳᠠᠷᠦ ᠢ᠄ ∠ CDH = 90° Rt ∆CDH ᠲᠤ᠂ ᠬ᠊ ᠤᠶᠠᠷ ᠡᠭᠴᠡ ᠲᠠᠯ ᠠ ᠶᠢᠨ ᠪᠠᠲᠤᠶ ᠤᠰᠤ ᠤ ᠠᠷ ᠤ ᠤᠳᠤᠭᠠ ᠳ᠋᠊ ᠣ ᠯᠬᠤ ᠨᠢ᠄ CH = √𝐶𝐷 2+ 𝐷𝐻 2= √ ︵2𝑘︶ 2 + 3 2 = √4 𝑘 2 + 9 ∴ BD = CH = √4 𝑘 2 + 9 24. ︵ᠲᠣᠰ ᠪᠠᠭ ᠠ ᠰ᠊ ᠡᠲᠥᠪ ᠨᠡᠢᠲᠡ 12 ᠬᠤᠪᠢ︶ ᠪᠤᠳᠤ ᠬᠤ ᠨᠢ᠄ ︵1︶ ᠴᠡ ᠬ᠋᠊ A ︵1 ,0︶ ,C ︵0 ,− 3︶ ᠶᠢ ᠲᠤᠰ ᠲᠤᠰ 𝑦= 𝑥 2 + 𝑏𝑥 + 𝑐 ᠲᠤ ᠣᠷᠣᠯ ᠠᠭᠤᠯ ᠤᠭᠠᠳ ᠣᠯᠬ ᠤ ᠨᠢ᠄ { 1 + 𝑏+ 𝑐= 0 𝑐= −3 ᠪᠤᠳᠤᠭᠠ ᠳ᠋᠊ ᠣ ᠯᠬᠤ ᠨᠢ { 𝑏 = 2 𝑐= −3 ∴ ᠲᠤᠰ ᠬᠠᠶ ᠠᠯᠲᠠ ᠶᠢᠨ ᠱᠤᠭᠤ ᠮ᠊ ᠤᠨ ᠠᠨᠠᠯ ᠢᠰ ᠢᠯᠡᠷ ᠬᠡᠢᠯ ᠡᠯ ᠨᠢ᠄ 𝑦 = 𝑥 2 + 2𝑥 − 3 ︵2︶ 𝑦 = 𝑥 2 + 2𝑥 − 3 ᠲᠤ y = 0 𝑥 2 + 2𝑥 − 3= 0 𝑥1 = −3᠂ 𝑥 2= 1 ∵A ︵1,0︶ ∴B ︵− 3,0︶ ∴OB = 3 ∴OB = OC = 3 ∵ ∠B OC = 90° ∴△ BO C ∴ ∠O BC = ∠O CB = 45° 45° ① D C BD 1 ∵∠ CB D1 = 15 ° , ∠O BC = 45° H E A B D C x y D 2 D 1 B A C O ∴∠ OB D1 = 30 ° ∴O D1 = 𝑂𝐵 ∙𝑡𝑎𝑛 30 º= √3 ∴C D1 = 𝑂𝐶 − 𝑂D 1= 3− √3 ② D C BD 2 ∵∠ CB D 2= 15° , ∠O BC = 45° ∴∠ OB D 2= ∠CB D 2+ ∠O BC = 60° ∴O D 2= 𝑂𝐵 ∙𝑡𝑎𝑛 60 °= 3√ 3 ∴C D 2= OD 2− 𝑂𝐶 = 3√ 3− 3 3− √3 3√ 3− 3 ︵3︶ AM = CM ∴∠ MA C= ∠A CO ∴∠ OMA = ∠M AC + ∠A CO = 2∠ AC O ∵∠ PAM = 2∠ AC O ∴∠ PAB = ∠OMA M ︵0 ,𝑚︶ A𝑀 2= 𝑚 2+ 1 M𝐶 2= ︵𝑚 + 3︶ 2 ∵AM = CM ∴ ︵𝑚 + 3︶ 2= 𝑚 2+ 1 ∴m = − 43 ∴OM = 43 ∴t an ∠OMA = OAOM = 34 ∴t an ∠P AB = tan ∠OMA = 34 ∵ y= 𝑥 2 + 2𝑥 − 3 ∴P ︵𝑡 ,𝑡 2+ 2𝑡 − 3︶ ① P x ∵t an ∠P AB = 34 ∴ 𝑡 2 :2t︔ 3 1︔ t = 34 ∵t ≠ 1 ∴ t= − 154 P ︵− 154 , 5716︶ ② P x ∵t an ∠P AB = 34 x y M P B A C O ∴︔ ︵𝑡 2 :2t︔ 3︶ 1︔ t = 34 ∵ t≠ 1 ∴ t= − 94 P ︵− 94 , 3916︶ ︵− 154 , 5716︶ ︵− 94 , 3916︶ AC M OM O OE ⊥ AC E Rt △ AO C ∵ ∴OM = CM = AM = 12 AC ∴∠ MOC = ∠A CO ∵∠ AMO = ∠MOC + ∠A CO ∴∠ AMO = 2∠ AC O ∵∠ PAB = 2∠ AC O ∴∠ AMO = ∠P AB ∵A ︵1 ,0︶ , 𝐶 ︵0,3︶ , ∴OA = 1 ,OC = 3 Rt △ AO C AC = √OA 2+ OC 2= √10 ∴OM = 12 AC = √1 02 ∵S △AO C= 12 AC ∙OE = 12 OA ∙OC ∴√ 10 OE = 1 × 3 ∴OE = 3√ 1010 Rt △ OEM EM = √OM 2− OE 2= √ 104 − 910 = 2√ 10 5 ∴t an ∠AMO = OEEM = 34 ∴t an ∠P AB = tan ∠AMO = 34 ∵ y= 𝑥 2 + 2𝑥 − 3 ∴P ︵𝑚 ,𝑚 2+ 2𝑚 − 3︶ PH ⊥ x PH = |𝑚 2+ 2m − 3|, AH = 1− m Rt △ PAH tan ∠P AB = PHAH = 34 ∴ |𝑚 2: 2m︔ 3 | 1︔ 𝑚 = 34 ∴ 𝑚 2: 2m︔ 3 1︔ 𝑚 = 34 𝑚 2: 2m︔ 3 1︔ 𝑚 = − 34 ∵m ≠ 1 m = − 154 m = − 94 ᠰᠢᠯᠭ ᠠᠬᠤ m = − 154 , m = − 94 x y P M B A C O x y E C B A H P O M x y E P B A C O M m = − 154 𝑚 2+ 2m − 3= 5716 m = − 94 𝑚 2+ 2m − 3= 3916 ∴ ︵− 154 , 5716︶ ︵− 94 , 3916︶ A′ CA′ AM ⊥ CA ′ ∠𝐴 ′CO = ∠A CO ,A ′C = AC ∴∠ 𝑃𝐴𝐵 = 2∠ 𝐴𝐶𝑂 ∴∠ 𝑃𝐴𝐵 = ∠𝐴 ′𝐶𝐴 ∵A ︵1 ,0︶ , 𝐶 ︵0, −3︶ , ∴A ′ ︵− 1,0︶ ∴OC = 3 , AC = √1 2+ 3 2 = √10 , 𝐴𝐴 ′= 2 A′C = AC = √10 ∵S △𝐴 ′𝐶𝐴 = 12 𝐴𝐴 ′∙ 𝑂𝐶 = 12 𝐴 ′𝐶 ∙𝐴𝑀 ∴ 12 × 2 × 3= 12 √ 10 ∙𝐴𝑀 ∴AM = 3√ 105 Rt △ ACB CM = √AC 2− AM 2= √10 − 185 = 4√ 105 ∴t an ∠𝐴𝐶 𝑀 = 𝐴𝑀𝐶𝑀 = 3√ 105 4√ 105 = 34 ∴t an ∠P AB = tan ∠𝐴 ′CA = 34 ∵ y= 𝑥 2 + 2𝑥 − 3 ∴P ︵𝑚 ,𝑚 2+ 2𝑚 − 3︶ P PH ⊥ x H PH = |𝑚 2+ 2m − 3|, AH = 1− m Rt △ PAH tan ∠P AB = PHAH = 34 ∴ |𝑚 2: 2m︔ 3 | 1︔ 𝑚 = 34 ∴ 𝑚 2: 2m︔ 3 1︔ 𝑚 = 34 𝑚 2: 2m︔ 3 1︔ 𝑚 = − 34 ∵m ≠ 1 m = − 154 m = − 94 ᠰᠢᠯᠭ ᠠᠬᠤ m = − 154 , m = − 94 m = − 154 𝑚 2+ 2m − 3= 5716 m = − 94 𝑚 2+ 2m − 3= 3916 x y M A' C B A H P O ∴ ︵− 154 , 5716︶ ︵− 94 , 3916︶ tan ∠P AB = 34 AP y E ∵t an ∠P AB = 34 , OA = 1 ∴OE = 34 , ∴ E ︵0 , 34︶ E ︵0 , − 34︶ ∵A ︵1 ,0︶ , E ︵0 , − 34︶ ∴ y= − 34 𝑥 + 34 y= 34 𝑥 − 34 y= 𝑥 2 + 2𝑥 − 3 { y = − 34 𝑥 + 34 y= 𝑥 2 + 2𝑥 − 3 { y = 34 𝑥 − 34 y= 𝑥 2 + 2𝑥 − 3 { 𝑥 1= 1 𝑦1 = 0 { 𝑥2 = − 154 𝑦2 = 5716 { 𝑥 3= 1 𝑦3 = 0 { 𝑥4 = − 94 𝑦4 = 3916 ∵A ︵1 ,0︶ ∴ ︵− 154 , 5716︶ ︵− 94 , 3916︶ x y E M A' C B A P O