16.1 ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ 1 ᠳ᠋ᠦ᠋ᠭᠡᠷ ᠦᠶ᠎ᠡ .pptx

16.1 ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ︵1︶ ᠳ᠋ᠦ᠋ᠭᠡᠷ ᠦᠶ᠎ᠡ , ᠨᠠᠢᠮᠠᠳᠤᠭᠠᠷ ᠣᠨ ︵ᠲᠤᠤᠷᠠᠳᠤ ᠲᠡᠪᠳᠡᠷ︶ , ᠠᠯᠪᠠᠨ ᠵᠢᠷᠤᠮ ᠤᠨ ᠰᠤᠷᠭᠠᠨ ᠭᠦᠮᠦᠵᠢᠯ ᠦᠨ ᠰᠤᠷᠬᠤ ᠪᠢᠴᠢᠭ , ᠲᠣᠭᠠᠨ ᠤ ᠤᠬᠠᠭᠠᠨ , ᠠᠷᠤ ᠬᠤᠷᠴᠢᠨ ᠬᠤᠰᠢᠭᠤᠨ ᠤ ᠴᠢᠪᠠᠭ᠎ᠠ ᠮᠣᠩᠭᠤᠯ ᠦᠨᠳᠦᠰᠦᠲᠡᠨ ᠤ ᠳᠤᠮᠳᠠᠳᠤ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ ᠦᠷᠴᠠᠢᠬᠤ , ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ , ᠪᠢᠳᠡ ᠵᠢᠷᠭᠤᠳᠤᠭᠠᠷ ᠪᠦᠯᠦᠭ ︿︿ᠪᠤᠳᠠᠳᠤ ᠲᠤᠭ᠎ᠠ﹀﹀ ᠳᠤ᠂ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ᠂ ᠲᠤᠭ᠎ᠠ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠶᠢᠨ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠤᠬᠠᠨᠳᠠᠬᠤᠨ ᠵᠢᠴᠢ ᠵᠡᠷᠭᠡ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠪᠤᠯᠤᠨ ᠢᠵᠠᠭᠤᠷ ᠭᠠᠷᠭᠠᠬᠤ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠨᠢ ᠬᠠᠷᠢᠯᠴᠠᠨ ᠤᠷᠪᠠᠭᠤ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠪᠤᠯᠬᠤ ᠶᠢ ᠠᠰᠢᠭᠯᠠᠨ ᠰᠦᠬᠡᠷᠬᠦ ᠪᠤᠰᠤ ᠲᠤᠭᠠᠨ ᠤ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ᠂ ᠲᠤᠭ᠎ᠠ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠶᠢᠨ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠢ ᠣᠯᠬᠤ ᠠᠷᠭ᠎ᠠ ᠶᠢ ᠰᠤᠷᠤᠯᠴᠠᠵᠠᠢ᠃ , ᠲᠤᠰ ᠪᠦᠯᠦᠭ ᠪᠢᠳᠡ ᠵᠢᠷᠭᠤᠳᠤᠭᠠᠷ ᠪᠦᠯᠦᠭ ᠤᠨ ᠰᠠᠭᠤᠷᠢᠨ ᠳᠡᠭᠡᠷ᠎ᠡ ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠤᠨ ᠤᠬᠠᠭᠳᠠᠬᠤᠨ᠂ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠪᠠ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠶᠢ ᠤᠯᠠᠮ ᠨᠢᠭᠡ ᠠᠯᠬᠤᠮ ᠬᠦᠨᠵᠡᠭᠡᠢ ᠰᠦᠪᠡᠭᠴᠢᠯᠡᠨ᠎ᠡ︔ , ᠶᠠᠭᠤ ᠶᠢ ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠭᠡᠬᠦ ᠪᠤᠢ︖ , ᠨᠢᠭᠡᠨ ᠡᠶᠡᠷᠭᠦ ᠲᠤᠭᠠᠨ ᠳᠤ ᠬᠤᠶᠠᠷ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠲᠠᠢ᠂ 0 ᠦᠨ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠨᠢ 0᠂ ᠰᠦᠬᠡᠷᠬᠦ ᠲᠤᠭᠠᠨ ᠳᠤ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠪᠠᠶᠢᠬᠤ ᠦᠬᠡᠢ᠃ , ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠤᠬᠠᠭᠳᠠᠬᠤᠨ :,𝑥 2 =𝑎 𝑎≥0,𝑥=±︔ 𝑎 ︵𝑎≥0︶ ,1 ᠲᠠᠯᠠᠪᠠᠢ ᠨᠢ 3 ᠪᠤᠯᠬᠤ ᠲᠡᠭᠰᠢ ᠲᠦ᠋ᠷᠪᠡᠯᠵᠢᠨ ᠦ ᠲᠠᠯ᠎ᠠ ᠶᠢᠨ ᠤᠷᠳᠤ ᠨᠢ ᠲᠠᠯᠠᠪᠠᠢ ᠨᠢ s ᠪᠤᠯᠬᠤ ᠲᠡᠭᠰᠢ ᠲᠦ᠋ᠷᠪᠡᠯᠵᠢᠨ ᠦ ᠲᠠᠯ᠎ᠠ ᠶᠢᠨ ᠤᠷᠳᠤ ᠨᠢ ,3,𝑠, ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ , ᠰᠡᠳᠬᠢᠬᠦ᠄ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠲᠡᠮᠳᠡᠭ ᠲᠠᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠢᠶᠠᠷ ᠬᠤᠭᠤᠰᠤᠨ ᠳᠤ ᠲᠠᠭᠯᠠ᠂ ᠪᠢᠴᠢᠭᠰᠡᠨ ᠳ᠋ᠦᠩ ᠴᠢᠨᠢ ᠶᠠᠮᠠᠷ ᠤᠨᠴᠠᠯᠢᠭ ᠲᠠᠢ ᠶᠢ ᠦᠵᠡ᠄ ,∵ 𝑎 2 =3 ∵𝑎0 ∴𝑎= 3,∵ 𝑎 2 =𝑠 ∵𝑎0 ∴𝑎= 𝑠, ︵2︶ ᠨᠢᠬᠡᠨ ᠤᠷᠳᠤ ᠲᠦ᠋ᠷᠪᠡᠯᠵᠢᠨ ᠬᠠᠰᠢᠶ᠎ᠠ ᠶᠢᠨ ᠤᠷᠳᠤ ᠨᠢ ᠦᠷᠭᠡᠨ ᠤ ᠪᠠᠨ 2 ᠲᠠᠭᠢᠨ᠂ ᠲᠠᠯᠠᠪᠠᠢ ᠨᠢ 130 𝑚 2᠂ ᠲᠡᠭᠦᠨ ᠤ ᠦᠷᠭᠡᠨ ᠨᠢ m ᠪᠤᠯᠤᠨ᠎ᠠ᠃ ,65,∵2𝑎∙𝑎=130 ∴ 𝑎 2 =65 ∵𝑎0 ∴𝑎= 65, ︵3︶ ᠨᠢᠭᠡᠨ ᠪᠡᠶ᠎ᠡ ᠦᠨᠳᠦᠷ ᠳᠡᠭᠡᠷ᠎ᠡ ᠠᠴᠠ ᠴᠢᠯᠦᠭᠡᠲᠠᠢ ᠤᠨᠠᠬᠤ ᠳᠤ᠂ ᠭᠠᠵᠠᠷ ᠳᠤ ᠳᠤᠰᠬᠤ ᠳᠤ ᠬᠡᠷᠡᠭᠯᠡᠬᠦ ᠬᠤᠭᠤᠴᠠᠭ᠎ᠠ t ︵ᠨᠢᠭᠡᠴᠢ᠄ s︶ ᠪᠠ ᠡᠬᠢᠯᠡᠨ ᠤᠨᠠᠬᠤ ᠦᠶᠡᠰ ᠤᠨ ᠦᠨᠳᠦᠷ ℎ ︵ᠨᠢᠭᠡᠴᠢ᠄ m︶ ᠨᠢ ᠬᠤᠯᠪᠤᠭᠳᠠᠯ ℎ=5 𝑡 2 ᠢ ᠬᠠᠩᠭᠠᠨ᠎ᠠ᠃ ᠬᠡᠷᠪᠡ ℎ ᠠᠭᠤᠯᠤᠠᠠᠰᠠᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠢᠶᠡᠷ 𝑡 ᠶᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠪᠡᠯ᠂ 𝑡 ᠨᠢ ᠪᠤᠯᠤᠨ᠎ᠠ᠃ ,ℎ 5, ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ , ᠰᠡᠳᠬᠢᠬᠦ᠄ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠲᠡᠮᠳᠡᠭ ᠲᠠᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠢᠶᠠᠷ ᠬᠤᠭᠤᠰᠤᠨ ᠳᠤ ᠲᠠᠭᠯᠠ᠂ ᠪᠢᠴᠢᠭᠰᠡᠨ ᠳ᠋ᠦᠩ ᠴᠢᠨᠢ ᠶᠠᠮᠠᠷ ᠤᠨᠴᠠᠯᠢᠭ ᠲᠠᠢ ᠶᠢ ᠦᠵᠡ᠄ ,∵ℎ=5 𝑡 2 ∴ 𝑡 2 = ℎ 5 ∵𝑡0 ∴𝑡= ℎ 5, ᠳᠡᠭᠡᠷᠡᠬᠢ ᠠᠰᠠᠭᠤᠳᠠᠯ ᠲᠠᠬᠢ 5, 𝑠, 65, ℎ 5 ᠨᠢ ᠬᠡᠳᠦᠨ ᠡᠶᠡᠷᠬᠦ ᠲᠤᠭᠠᠨ ᠤ ᠲᠤᠭ᠎ᠠ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠶᠢᠨ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠨ᠎ᠡ᠃ , ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ , ᠮᠡᠳᠡᠭᠡᠵᠢ ᠪᠠᠷ᠂ ᠨᠢᠭᠡᠨ ᠡᠶᠡᠷᠭᠦ ᠲᠤᠭᠠᠨ ᠳᠤ ᠬᠤᠶᠠᠷ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠲᠠᠢ᠂ 0 ᠦᠨ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠨᠢ 0᠂ ᠪᠤᠳᠠᠳᠤ ᠲᠤᠭᠠᠨ ᠤ ᠬᠡᠪᠴᠢᠶᠡᠨ ᠳᠤ᠂ ᠰᠦᠬᠡᠷᠬᠦ ᠲᠤᠭᠠᠨ ᠳᠤ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠪᠠᠶᠢᠬᠤ ᠦᠬᠡᠢ᠃ ᠡᠶᠢᠮᠦ ᠠᠴᠠ ᠪᠤᠳᠠᠳᠤ ᠲᠤᠭᠠᠨ ᠤ ᠬᠡᠪᠴᠢᠶᠡᠨ ᠳᠤ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠭᠠᠷᠭᠠᠬᠤ ᠦᠶᠡᠰ᠂ ᠢᠵᠠᠭᠤᠷ ᠭᠠᠷᠭᠠᠭᠳᠠᠬᠤ ᠲᠤᠭ᠎ᠠ ᠨᠢ ᠵᠦᠪᠬᠡᠨ ᠡᠶᠡᠷᠬᠦ ᠲᠤᠭ᠎ᠠ ᠪᠤᠶᠤ 0 ᠪᠤᠯᠤᠨ᠎ᠠ᠃ ,1. ᠠᠯᠢ ᠠᠯᠢ ᠨᠢ ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠦᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠪᠤᠢ︖ ,,−2 , 𝑚 𝑚0 , 0 , −𝑛 𝑛0,𝑚 𝑚0 ,,0 ,,−𝑛 𝑛0 ,,𝑎 2 +1 ,,16, ᠬᠢᠵᠤ ᠦᠵᠡᠶ᠎ᠡ , ︵1︶ 𝑥−2, ᠵᠢᠱᠢᠶ᠎ᠡ 1:, ᠪᠤᠳᠤᠬᠤ ᠨᠢ᠄ , ᠲᠠᠢ ᠪᠤᠢ︖ ᠨᠢ ᠤᠳᠬ᠎ᠠ ᠢᠯᠡᠷᠭᠡᠢᠯᠡᠯ ᠲᠤᠤᠷᠠᠭᠢ ᠦᠶᠡᠰ᠂ ᠪᠤᠳᠠᠳᠤ ᠲᠤᠭ᠎ᠠ 𝑥 ᠨᠢ ᠶᠠᠮᠠᠷ , ︵2︶ 𝑥 2, ︵3︶ 𝑥 3, ︵1︶ , ︵2︶ , ︵3︶ ,∴ x ≥ 0, ᠪᠠᠳᠤᠳᠬᠠᠯ ᠪᠤᠯᠪᠠᠰᠤᠷᠠᠯ ,∵𝒂−𝟏≥0 ∴𝒂 ≥ 𝟏,∵𝟐𝒂+𝟑≥𝟎 𝟐𝒂≥−𝟑 ∴𝒂≥− 𝟑 𝟐,∵−𝒂≥𝟎 ∴𝒂≤𝟎,∵𝟓−𝒂≥𝟎∴𝒂≤𝟓, ︵1︶ 𝒂−𝟏, ︵2︶ 𝟐𝒂+𝟑, ︵3︶ −𝒂, ︵4︶ 𝟓−𝒂,1.𝑎 ᠨᠢ ᠶᠠᠮᠠᠷ ᠪᠤᠳᠠᠳᠤ ᠲᠤᠭ᠎ᠠ ᠦᠶᠡᠰ᠂ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠡᠯ᠎ᠡ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠨᠢ ᠪᠤᠳᠠᠳᠤ ᠲᠤᠭᠠᠨ ᠤ ᠭᠡᠪᠴᠢᠶᠡᠨ ᠳᠤ ᠤᠳᠬ᠎ᠠ ᠲᠠᠢ ᠪᠤᠢ︖ , ᠬᠢᠴᠢᠶᠡᠯ ᠤᠨ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠪᠤᠯᠪᠠᠰᠤᠷᠠᠯ ᠤᠨ ᠰᠡᠳᠦᠪ , ᠳᠠᠷᠠᠭᠠᠬᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠨᠢ ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠮᠦᠨ ᠡᠰᠡᠬᠦ ᠶᠢ ᠮᠠᠭᠠᠳᠯᠠᠶ᠎ᠠ᠃ ,① 32 ②6 ③ 9 ④ 3 5 ⑤ −12 ⑥ 𝑎 2 ⑦ │𝑎│+1 ⑧ 𝑎 2 + 𝑏 2 ⑨ 2𝑚+5 ⑩ − 𝑥 2 −4 ⑪ 𝑥 2 +2𝑥𝑦+ 𝑦 2 ⑫ − 𝑥 2 +2𝑥𝑦− 𝑦 2,2. X ᠨᠢ ᠶᠠᠮᠠᠷ ᠬᠡᠮᠵᠢᠭᠳᠡᠯ ᠠᠪᠬᠤ ᠦᠶᠡᠰ᠂ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠨᠢ ᠪᠤᠳᠠᠳᠤ ᠲᠤᠭᠠᠨ ᠤ ᠬᠡᠪᠴᠢᠶᠡᠨ ᠳᠤ ᠤᠳᠬ᠎ᠠ ᠲᠠᠢ ᠪᠤᠯᠬᠤ ᠪᠤᠢ︖ ,❶ 𝑥 2 +1 ❷ 1 𝑥 ❸ −𝑥 ❹ 𝑥 2 +2𝑥+3 ❺ 𝑎−1 2 ❻ − 𝑎−1 2 ❼ 𝑎 2 −2𝑎+2 ❽ −2 2𝑥−4 ❾ 1 𝑥−1 2 ❿ 𝑥+1 𝑥−3 2, ᠳ᠋ᠦ᠋ᠩᠨ᠋ᠡᠯᠳᠡ᠄ ,1. ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠦᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠦᠨ ᠤᠬᠠᠭᠳᠠᠬᠤᠨ 2. ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠦᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠤᠨ ᠢᠵᠠᠭᠤᠷ ᠭᠠᠷᠭᠠᠠᠠᠳᠠᠬᠤ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠲᠠᠬᠢ ᠦᠰᠦᠭ ᠦᠨ ᠬᠡᠮᠵᠢᠭᠳᠡᠯ ᠠᠪᠬᠤ ᠬᠡᠪᠴᠢᠶ᠎ᠡ᠃ ,