16.1 ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ （2） .pptx

16.1 ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ︵2︶ ᠳ᠋ᠤᠭᠠᠷ 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 , ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ 1,𝑎 ≥0, ᠰᠦᠬᠡᠷᠬᠦ ᠪᠤᠰᠤ ᠲᠤᠭᠠᠨ ᠤ ᠲᠤᠭ᠎ᠠ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠶᠢᠨ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠨᠢ ᠪᠠᠰᠠ ᠰᠦᠬᠡᠷᠬᠦ ᠪᠤᠰᠤ ᠲᠤᠭ᠎ᠠ ᠪᠤᠯᠤᠨ᠎ᠠ᠃ ,𝑎,𝑎≥0,𝑎≥0, ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠤᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ,│𝑎−5│+ 𝑏−2 + 𝑐−3 2 =0,𝑎−𝑏+𝑐=, ᠲᠡᠭᠡᠪᠡᠯ ,│𝑎│≥0,𝑎 ≥0,𝑎 2 ≥0,,𝑎−5=0,𝑏−2=0,𝑐−3=0,,,c=3,𝑎=5,b=2,,𝑎−𝑏+𝑐=6, ᠬᠢᠵᠤ ᠦᠵᠡᠶ᠎ᠡ , ︵4︶ 2 =,=4, ︵𝑎︶ 2 = 𝑎 ∙ 𝑎 =𝑎 ︵𝑎≥0︶ , ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ 2,4 ∙ 4, ︵5︶ 2 =,5,𝑥 2 =5,𝑥= 5, ᠨᠢᠭᠡᠨ ᠲᠤᠭᠠᠨ ᠤ ᠲᠤᠭ᠎ᠠ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠶᠢᠨ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠺᠦᠸᠠᠳ᠋ ᠨᠢ ᠲᠡᠭᠦᠨ ᠤ ᠢᠵᠠᠭᠤᠷ ᠭᠠᠷᠭᠠᠭᠳᠠᠬᠤ ᠲᠤᠭ᠎ᠠ ᠲᠠᠢ ᠲᠡᠩᠴᠡᠭᠦᠤ᠃ , ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠤᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ , ᠬᠢᠵᠤ ᠦᠵᠡᠶ᠎ᠡ ,1 3 2 =,2 2 5 2 =,𝑎𝑏 2 = 𝑎 2 𝑏 2,2 2 ×︔ 5 2,=4×︔ 5 =20,3,4 2 = −4 2 = 0 2 =,4,4,𝑎 2 =│𝑎│, ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ 3, ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠤᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ , ᠨᠢᠭᠡᠨ ᠲᠤᠭᠠᠨ ᠤ ᠺᠦᠸᠠᠳ᠋ ᠤᠨ ᠲᠤᠭ᠎ᠠ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠶᠢᠨ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠨᠢ ᠡᠨᠡ ᠲᠤᠭ᠎ᠠ ᠨᠢ ᠡᠶᠡᠷᠬᠦ ᠪᠤᠯ ᠡᠨᠡ ᠲᠤᠭ᠎ᠠ ᠲᠠᠢ ᠲᠡᠩᠴᠡᠭᠦᠤ᠃ ᠰᠦᠬᠡᠷᠬᠦ ᠲᠤᠭ᠎ᠠ ᠪᠤᠯ ᠲᠡᠭᠦᠨ ᠤ ᠡᠰᠡᠷᠬᠦ ᠲᠤᠭ᠎ᠠ ᠲᠠᠢ ᠲᠡᠩᠴᠡᠭᠦᠤ᠃ 0 ᠪᠤᠯ ᠲᠡᠭ ᠪᠤᠯᠤᠨ᠎ᠠ᠃ ,0,𝑎 2 = 𝑎, ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ 3,,𝑎0,𝑎=0,𝑎0, ᠨᠢᠭᠡᠨ ᠲᠤᠭᠠᠨ ᠤ ᠺᠦᠸᠠᠳ᠋ ᠤᠨ ᠲᠤᠭ᠎ᠠ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠶᠢᠨ ᠺᠦᠸᠠᠳ᠋ ᠢᠵᠠᠭᠤᠷ ᠨᠢ ᠡᠨᠡ ᠲᠤᠭ᠎ᠠ ᠨᠢ ᠡᠶᠡᠷᠬᠦ ᠪᠤᠯ ᠡᠨᠡ ᠲᠤᠭ᠎ᠠ ᠲᠠᠢ ᠲᠡᠩᠴᠡᠭᠦᠤ᠃ ᠰᠦᠬᠡᠷᠬᠦ ᠲᠤᠭ᠎ᠠ ᠪᠤᠯ ᠲᠡᠭᠦᠨ ᠤ ᠡᠰᠡᠷᠬᠦ ᠲᠤᠭ᠎ᠠ ᠲᠠᠢ ᠲᠡᠩᠴᠡᠭᠦᠤ᠃ 0 ᠪᠤᠯ ᠲᠡᠭ ᠪᠤᠯᠤᠨ᠎ᠠ᠃ ,𝑎,0,−𝑎, ᠬᠢᠵᠤ ᠦᠵᠡᠶ᠎ᠡ ,1 5 2 =,2 − 1 7 2 =,3 3−π 2,4 1− 2 2,=│3−𝜋│,=𝜋−3,=│1− 2 │,= 2 −1,5,1 7, ᠠᠯᠭᠧᠪᠷᠡ ᠶᠢᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ,5,𝑎,𝑎𝑏,−𝑎𝑏, 𝑠 𝑡 ,− 𝑥 3 , 3 , 𝑎 𝑎≥0 ᠮᠡᠲᠦ ᠶᠢᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠢ ᠡᠷᠬᠢᠴᠡᠭᠦᠯᠪᠡᠯ᠂ ᠲᠡᠳᠡᠭᠡᠷ ᠨᠢ ᠴᠦᠮ ᠦᠨᠳᠦᠰᠦᠨ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠶᠢᠨ ᠲᠡᠮᠳᠡᠭ ︵ᠦᠨᠳᠦᠰᠦᠨ ᠪᠤᠳᠤᠯᠭ᠎ᠠ ᠳᠤ ᠨᠡᠮᠡᠬᠦ᠂ ᠬᠠᠰᠤᠬᠤ᠂ ᠦᠷᠡᠵᠢᠭᠦᠯᠬᠦ᠂ ᠬᠤᠪᠢᠶᠠᠬᠤ᠂ ᠵᠡᠷᠭᠡ ᠳᠡᠪᠰᠢᠭᠦᠯᠬᠦ ᠪᠠ ᠢᠵᠠᠭᠤᠷ ᠭᠠᠷᠭᠠᠬᠤ ᠪᠠᠭᠲᠠᠨ᠎ᠠ︶ ᠢᠶᠠᠷ ᠲᠤᠭ᠎ᠠ ᠪᠠ ᠲᠤᠭ᠎ᠠ ᠶᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠭᠰᠡᠨ ᠦᠰᠦᠭ ᠢ ᠬᠤᠯᠪᠤᠭᠰᠠᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠪᠤᠯᠤᠨ᠎ᠠ᠂ ᠪᠢᠳᠡ ᠡᠶᠢᠮᠦᠷᠬᠦᠤ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠢ ᠠᠯᠭᠧᠪᠷᠡ ᠶᠢᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠭᠡᠨ᠎ᠡ᠃ , ᠠᠯᠭᠧᠪᠷᠡ ᠶᠢᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ,, ᠪᠦᠬᠦᠯᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ , ᠪᠤᠲᠠᠷᠬᠠᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ , ᠬᠤᠶᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠢᠵᠠᠭᠤᠷ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ,4,𝑎,5𝑥+𝑝, 𝑥 2 -7,⋯,4 𝑎 𝑎≠0 , 1 𝑥−3 𝑥≠3 ,⋯,𝑎 𝑎≥0 , 𝑥+3 𝑥≥−3 , 𝑥 2 +1 5 ,⋯,① ᠳᠠᠩ ᠭᠠᠭᠴᠠ ᠨᠢᠭᠡ ᠲᠤᠭ᠎ᠠ ᠪᠤᠶᠤ ᠨᠢᠭᠡ ᠦᠰᠦᠭ ᠨᠢ ᠮᠦᠨ ᠴᠤ ᠠᠯᠭᠧᠪᠷᠡ ᠶᠢᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠪᠤᠯᠤᠨ᠎ᠠ᠃ ② ᠠᠯᠭᠧᠪᠷᠡ ᠶᠢᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠲᠤᠮᠳᠠ ᠲᠡᠮᠳᠡᠭ =≠≤≥≈ ᠠᠭᠤᠯᠵᠤ ᠪᠤᠯᠬᠤ ᠦᠭᠡᠢ᠃ ③ ᠬᠡᠷᠪᠡ ᠬᠤᠶᠠᠷ ᠠᠯᠭᠧᠪᠷᠡ ᠶᠢᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠢ ᠲᠡᠮᠳᠡᠭ ︵=᠂ ≠᠂᠂ ≤᠂ ≥᠂ ≈︶ ᠪᠠᠷ ᠬᠤᠯᠪᠤᠪᠠᠯ ᠲᠡᠷᠡ ᠨᠢ ᠬᠤᠯᠪᠤᠭᠳᠠᠯ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠪᠤᠯᠤᠨ᠎ᠠ᠃ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠪᠠ ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠤᠰᠤ ᠨᠢ ᠴᠦᠮ ᠬᠤᠯᠪᠤᠭᠳᠠᠯ ᠤᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠮᠦᠨ᠃ , ᠠᠩᠬᠠᠷᠬᠤ᠄ , ᠠᠯᠭᠧᠪᠷᠡ ᠶᠢᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ , ᠳᠠᠷᠠᠭᠠᠬᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠳᠤ ①0 ② 𝜋 2 ③3+x=5 ④ 𝑥−2 3 1 ⑤2𝑎+5𝑏 ⑥ 𝑥−3 𝑥≥3 ᠡᠭᠦᠨ ᠳᠤ ᠠᠯᠭᠧᠪᠷᠡ ᠶᠢᠨ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠯ ᠨᠢ ︵︶ ᠪᠠᠶᠢᠨ᠎ᠠ , ᠬᠢᠵᠤ ᠦᠵᠡᠶ᠎ᠡ , ᠳ᠋ᠦ᠋ᠩᠨ᠋ᠡᠯᠳᠡ᠄ , ︵𝑎︶ 2 =𝑎 , ︵𝑎≥0︶ ,𝑎 2 = 𝑎 ︵𝑎≥ 0︶ ,𝑎 2 =－𝑎 ︵𝑎＜0︶ ,𝑎 2 = 𝑎,𝑎≥0 𝑎 ≥0, ᠪᠠᠳᠤᠳᠬᠠᠯ ᠪᠤᠯᠪᠠᠰᠤᠷᠠᠯ , ᠪᠤᠳᠤ ,1 7 2 2 − 0.2 2 3 2 7 2 4 5 5 2 5 −10 2 6 −7 2 7 2 7 − 2 3 2 8 − − 2 5 2, ᠦᠷᠭᠡᠳᠬᠡᠯ ᠪᠤᠯᠪᠠᠰᠤᠷᠠᠯ ,1. ᠬᠢᠯᠪᠠᠷᠴᠢᠯᠠ᠄ ,4 𝑥 2 −12𝑥+9 − 4 𝑥 2 −20𝑥+25 3 2 𝑥 5 2,= 2𝑥−3 2 − 2𝑥−5 2,=2𝑥−3− 5−2𝑥,=2𝑥−3−5+2𝑥,=4𝑥−8,2. ᠬᠢᠯᠪᠠᠷᠴᠢᠯᠠ᠄ ,∣1−𝑎∣+ 𝑎 2 −6𝑎+9 1𝑎2,=− 1−𝑎 + 𝑎−3 2,=−1+𝑎+ − 𝑎−3,=−1+𝑎+3−𝑎,=2,