ᠠᠷᠪᠠᠨ ᠲᠦᠷᠪᠡᠳᠤᠭᠡᠷ ᠪᠦᠯᠦᠭ ᠪᠦᠬᠦᠯᠢ ᠢᠯᠡᠷᠭᠡᠢᠯᠡᠯ ᠤᠨ ᠦᠷᠡᠵᠢᠬᠦᠯᠬᠦ ᠤᠢᠯᠡᠳᠤᠯ ᠬᠢᠭᠡᠳ ᠦᠷᠡᠵᠢᠭᠳᠡᠬᠦᠨ ᠪᠤᠯᠭᠠᠨ ᠵᠠᠳᠠᠯᠬᠤ （ᠨᠢᠭᠡᠴᠢ ᠶᠢᠨ ᠪᠠᠢᠴᠠᠭᠠᠯᠲᠠ 1） .pdf

ᠠᠷᠪ ᠠᠨ ᠳ ᠦᠷᠪ ᠡᠳᠦᠭ ᠡᠷ ᠪᠥᠯ ᠥᠭ ᠦ ᠨ ᠪᠠ ᠢᠴᠠ ᠭᠠᠯᠲ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯᠥᠭ᠄ ᠨᠡᠷ ᠡ ᠄ ︵90 ᠮ ᠢᠨᠦ᠋ᠲ ᠂ ᠨᠠᠢ ᠲᠡ 120 ᠬᠤ ᠪᠢ ︶ ᠨᠢᠭᠡ ᠂ ᠰ ᠤᠩᠭᠤ ᠬᠤ ᠰ ᠡᠲᠤᠪ ᠃ ︵ ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 30 ᠬᠤ ᠪᠢ ︶ 1. ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠪᠣ ᠳᠣᠯᠭ ᠠ ᠳᠤ ᠳᠦ᠋ ᠩ ᠨ ᠢ 𝑎 5 ᠪ ᠣᠯᠬᠤ ᠨᠢ ( ) A. 𝑎 10 ÷ 𝑎 2 B. (𝑎 2) 3 C. (− 𝑎) 5 D. 𝑎 3∙ 𝑎 2 2. ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠪᠣ ᠳᠣᠯᠭ ᠠ ᠠᠴ ᠠ ᠵᠥ ᠪ ᠪᠣ ᠯᠬᠤ ᠨᠢ ( ) A. 𝑎 2+ 2𝑎 = 3𝑎 3 B. (− 2𝑎 3) 2= 4𝑎 5 C. (𝑎 + 2) (𝑎 − 1) = 𝑎 2 + 𝑎− 2 D. (𝑎 + 𝑏) 2= 𝑎 2 + 𝑏 2 3. ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠪᠣ ᠳᠣᠯᠭ ᠠ ᠠᠴ ᠠ ᠵ ᠥᠪ ᠪ ᠣᠯᠬᠤ ᠨᠢ ( ) A. (− 5𝑎 2𝑏 )(− 3𝑎 )= 15 𝑎 2 𝑏 B. (− 𝑎 2 𝑏) 3= 𝑎 6 𝑏 3 C. 4𝑎 4÷ 2𝑎 3= 12 𝑎 D. (√ 2) 2− 4 0 = 1 4. ᠳᠠᠷᠠᠭᠠᠬ ᠢ ᠢᠯᠡᠷᠬ ᠡᠢᠯᠡᠯ ᠳᠤ ᠲᠤᠷ ᠠ ᠠᠴᠠ ᠣᠯᠠᠨᠭᠡᠰᠢ ᠭᠦᠨᠲ ᠦ2 𝑥 2 − 4𝑥 + 2 ᠢᠢ ᠦᠷᠡᠵ ᠢᠭᠳᠡᠬ ᠦ ᠪ ᠢᠰᠢ ᠨ ᠢ ( ) A. 2 B. 2( 𝑥− 1) C. (𝑥 − 1) 2 D. 2( 𝑥− 2) 5. ᠦᠭ ᠬᠦᠭᠳ ᠡᠭᠰᠡ ᠨᠢ 𝑥 2− 𝑦 2 = 2 ᠪᠣᠯ (4 𝑥− 𝑦) 𝑥+ 𝑦 ᠢ ᠢ ᠡᠡᠵᠵᠢ ᠭᠳᠡᠯ ᠨᠢ ( ) A. 8 B. 10 C. 12 D. 16 6. ᠨᠢᠭᠡ ᠭᠤᠷᠪᠠ ᠯᠵᠢ ᠦ ᠰ ᠠᠭᠤᠷᠢ ᠢᠢ ᠤᠷᠳ ᠤ ᠨᠢ 2 𝑥 2 𝑦+ 𝑥𝑦 − 𝑦 2 ,ᠰᠠᠭᠤ ᠷᠢ ᠳᠡᠭᠡ ᠷᠡᠬᠢ ᠦᠨᠳ ᠦᠷ ᠨ ᠢ 6 𝑥𝑦 ᠂ ᠲ ᠡᠭᠡᠪᠡᠯ ᠡᠨᠡᠬ ᠦ ᠭᠤ ᠷᠪᠠᠯ ᠵᠢ ᠤ ᠲ ᠠᠯᠠᠪᠠ ᠢ ᠨᠢ ( ) A. 6𝑥 3𝑦 2+ 3𝑥 2𝑦 2− 3𝑥 𝑦 3 B. 6𝑥 2𝑦 2+ 3𝑥𝑦 − 3𝑥 𝑦 2 C. 6𝑥 2𝑦 2+ 3𝑥 2𝑦 2− 𝑦 2 D. 6𝑥 2𝑦 + 3𝑥 2𝑦 2 7. ᠦᠷᠡᠵ ᠢᠭᠳᠡᠬ ᠦ ᠪ ᠤᠯᠭᠠ ᠵᠠᠳ ᠠᠯᠤᠭᠰᠠ ᠠᠴᠠ ᠵ ᠦ᠋ᠪ ᠪ ᠣᠯᠬᠤ ᠨᠢ ( ) A. 2𝑥 2− 6𝑥 = 2𝑥 (𝑥 − 6) B. − 𝑎 3 + 𝑎𝑏 = −𝑎 (𝑎 2− 𝑏) C. − 𝑥 2 − 𝑦 2 = −( 𝑥+ 𝑦) (𝑥 − 𝑦) D. 𝑚 2− 9𝑛 2= (𝑚 + 9𝑛 )(𝑚 − 9𝑛 ) 8. ᠡᠡᠷᠪᠡ −3 𝑥 2 (2 𝑥+ [ ] + 1) = −6 𝑥 3 + 6𝑥 2𝑦 − 3𝑥 2 ᠪᠣᠯ᠂ [ ] ᠳᠤ ᠲᠤᠷ ᠠ ᠲ ᠠᠭᠯᠠᠬᠤ ᠨᠢ ( ) A. − 𝑦 B. − 2𝑦 C. 2𝑦 D. 2𝑥𝑦 9. ᠡᠡᠷᠪᠡ 2 𝑚 = 5 , 4 𝑛= 3 ᠪ ᠣᠯ᠂ 4 3 𝑛− 𝑚 ᠢ ᠢ ᠡ ᠡᠵᠵᠢᠭ ᠳᠡᠯ ᠨ ᠢ ( ) A. 910 B. 2725 C. 2 D. 4 10. 𝑎 ,𝑏 ,𝑐 ᠨᠢ ᠭᠤᠷᠪᠠ ᠯᠵᠢ ᠤ ᠭ ᠤᠷᠪᠠ ᠲ ᠠᠯ ᠠ ᠢᠢ ᠤᠷᠳ ᠤ᠂ ᠲ ᠡᠭᠡᠪᠡᠯ (𝑎 − 𝑏) 2− 𝑐 2 ᠢᠢ ᠡᠡᠵᠵ ᠢᠭᠳᠡᠯ ᠨᠢ ( ) A. ᠲᠡᠭ ᠡᠴᠡ ᠶ ᠡᠭᠡ B. ᠲᠡᠭ ᠡᠴᠡ ᠪᠠ ᠭ ᠠ C. ᠲᠡᠭ ᠲᠠᠢ ᠲ ᠡᠩᠴ ᠡᠬᠦᠦ D. ᠲᠤ ᠭᠲᠠᠭᠠᠵ ᠤ ᠲ ᠡᠢᠯᠬ ᠦ ᠦᠭᠡᠢ ᠬᠣᠶ ᠠᠷ᠂ ᠬᠠᠭᠠ ᠯᠲᠠ ᠳ ᠤ ᠲ ᠠᠭᠯᠠᠬᠤ ᠰᠡᠲᠤ ᠪ᠃ ︵ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ ᠂ ᠨ ᠠᠢᠲ ᠡ 24 ᠬᠤ ᠪᠢ ︶ 11. 3𝑥 2𝑦𝑧 + 15 𝑥𝑧 2− 9𝑥 𝑦 2 𝑧 ᠦᠷᠡᠵ ᠢᠭᠳᠡᠬ ᠦ ᠪᠤᠯᠭᠠ ᠵ ᠠᠳᠠᠯᠪᠠ ᠯ _________ 12. ᠪᠠ ᠳᠦ ᠰᠢᠨ ᠡ ᠪᠠ ᠢᠰᠢ ᠩ ᠬᠤᠳ ᠠᠯᠳᠤ ᠠᠪᠤ ᠪᠠ᠂ ᠥᠷᠥ ᠭᠡ ᠦ ᠲᠠᠢ ᠯᠪᠤᠷᠢ ᠵᠢᠷᠤᠭ ᠨᠢ ᠵᠢᠷᠤᠭ ᠲᠤ ᠦᠵᠡᠬ ᠦᠯᠦᠭᠰᠡ ᠮᠡᠳ ᠤ᠂ ᠪᠠᠲᠤ ᠭᠡᠷ ᠦ ᠢ ᠶᠡ ᠤᠨᠳ ᠠᠬᠤ ᠦᠷᠦ ᠭᠡ ᠳᠡᠬᠡ ᠮᠤ ᠳᠤ ᠱ ᠠᠯᠠ ᠬ ᠠᠪᠲᠠ ᠰᠤ ᠳᠡᠪᠢ ᠰᠴᠦ᠂ ᠪᠤ ᠰᠤᠳ ᠦᠷᠦ ᠭᠡ ᠳᠡᠬᠡ ᠱ ᠠᠭᠠᠵᠠ ᠩ ᠱᠠᠯᠠ ᠬ ᠠᠪᠲᠠ ᠰᠤ ᠳᠡᠪᠢ ᠰᠬᠦ ᠪᠡᠷ ᠲ ᠦ᠋ᠯᠦᠪᠯ ᠡᠪᠡ᠃ ᠲᠡᠭᠡᠪᠡᠯ ᠪᠠᠳ ᠦ ᠪᠡᠯ ᠡᠳᠭᠡᠬ ᠦ ᠴ ᠢᠬᠤᠯ ᠠᠳᠠᠢ ᠮᠤ ᠳᠤ ᠱᠠᠯ ᠠ ᠬᠠᠪᠲ ᠠᠰᠤ ᠢᠢ ᠲᠠᠯᠠᠪᠠ ᠢ ᠨᠢ__________ 13. ᠦᠭ ᠬᠦᠭᠳ ᠡᠭᠰᠡ ᠨᠢ A = 12 34 56 × 12 34 57 ,B = 12 34 57 2 ᠪ ᠣᠯ A ᠪᠠ B ᠢᠢ ᠶᠡᠬ ᠡ ᠪᠠ ᠭ ᠠ ᠢᠢ ᠠ ᠳᠠᠯᠢ ᠳᠬᠠᠪᠠ ᠯ᠄ A ____ B 14. ᠡᠡᠷᠪᠡ mn = 3 , 𝑎+ 𝑏= 4 , 𝑎− 𝑏= 5 ᠲᠡᠭᠡᠪᠡᠯ mn 𝑎 2 − mn 𝑏 2 ᠦ ᠡᠡᠵᠵᠢ ᠭᠳᠡᠯ ᠨ ᠢ_____ _ 15. ᠡᠡᠷᠪᠡ 𝑥 2 + 16 𝑥− 𝑘 ᠨᠢ ᠨᠢᠭᠡ ᠭᠦᠢ ᠴᠡᠳ ᠺᠦᠸᠠᠳ᠋ ᠤ ᠢᠯᠡᠷᠭᠡᠢ ᠯᠡᠯ ᠪᠣᠯ k= ____ 16. ᠦᠷᠡᠵ ᠢᠭᠳᠡᠬ ᠦ ᠪ ᠤᠯᠭᠠ ᠵᠠᠳ ᠠᠯ᠄ −3m 𝑎 2 + 12m 𝑎− 12 m =______ 17. ᠦᠭ ᠬᠦᠭᠳ ᠡᠭᠰᠡ ᠨᠢ ᠡᠶᠡᠷ ᠬᠦ ᠲ ᠤᠭ ᠠ 𝑎 ,𝑏 ,𝑐 ᠨᠢ ∆AB C ᠢᠢ ᠭᠤᠷᠪᠠ ᠲ ᠠᠯ ᠠ ᠢᠢ ᠤᠷᠳ ᠤ ᠪᠦᠭᠡᠳ ᠲ ᠡᠩᠴ ᠡᠳᠬᠡᠯ 𝑎 2 − 𝑐 2 + 𝑎𝑏 − 𝑏𝑐 = 0 ᠪᠠᠢ ᠭᠤᠯᠤ ᠭᠳᠠᠨ ᠠ᠂ ᠲᠡᠭᠡᠪᠡᠯ ∆AB C ᠨ ᠢ________ ᠭᠤ ᠷᠪᠠᠯ ᠵᠢ ᠪᠤᠯ ᠤᠨ ᠠ ᠃ 18. ᠨᠢᠭᠡ ᠡᠡᠯ ᠪᠡᠷᠢ ᠨᠢ 𝑥 2 + 𝑝𝑥 + 𝑞 ᠪ ᠣᠯᠬᠤ ᠬᠤᠶ ᠠᠳᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠢᠢ ᠭᠤ ᠷᠪᠠᠨᠭᠡᠰᠢ ᠭᠦᠨᠲ ᠦ ᠢᠢ ᠦᠷᠡᠵ ᠢᠭᠳᠡᠬ ᠦ ᠪᠣᠯᠭᠠ ᠵᠠᠳ ᠠᠯᠬᠤ ᠦᠶ ᠡᠰ ᠡᠡᠷᠪᠡ 𝑞= mn ᠪᠦᠭᠡᠳ 𝑝 = m + n ᠪᠣᠯ 𝑥 2 + 𝑝𝑥 + 𝑞 ( x+ m) (x + n) ᠭᠡᠵᠦ ᠦᠷᠡ ᠵᠢᠭᠳ ᠡᠬᠦ ᠪᠤ ᠯᠭᠠ ᠵ ᠠᠳᠠᠯᠤ ᠨ ᠠ᠃ ᠵᠢᠱᠢ ᠶᠡᠯᠡᠪᠡᠯ ᠄ ( 1) 𝑥 2 + 3𝑥 + 2= (𝑥 + 1) (𝑥 + 2) , (2) 𝑥 2 − 3𝑥 − 10 = (𝑥 − 5) (𝑥 + 2) ᠪᠤ ᠯᠤᠨ ᠠ᠃ ᠲ ᠡᠭᠡᠪᠡᠯ ᠬ ᠤᠶᠠᠳ ᠤᠭᠠᠷ ᠵᠡᠷᠭᠡ ᠢᠢ ᠭ ᠤᠷᠪᠠ ᠨᠭᠡᠰᠢ ᠭᠦᠨᠲ ᠦ 𝑥 2 + 𝑚𝑥 − 6 ᠢᠢ ᠪ ᠦᠬᠦᠯ ᠢ ᠲ ᠣᠭᠠ ᠤ ᠡ ᠡᠪᠴᠢ ᠶᠡ ᠳᠦ ᠦᠷᠡᠵ ᠢᠭᠳᠡᠬ ᠦ ᠪᠤᠯᠭᠠ ᠵᠠᠳ ᠠᠯᠪᠠᠯ 𝑚 ᠢᠢ ᠠᠪᠴᠤ ᠪ ᠣᠯᠬᠤ ᠪᠦᠬᠦ ᠯᠢ ᠲ ᠣᠭᠠ ᠡᠡᠵᠵ ᠢᠭᠳᠡᠯ ᠨ ᠢ___ ______ ______ ᠭᠤᠷᠪᠠ᠂ ᠪᠣᠳ ᠣᠵᠤ ᠬᠠᠷᠢ ᠭᠤᠯᠬᠤ ᠰᠡᠲᠤ ᠪ᠃ ( ᠨᠠᠢ ᠲᠡ 66 ᠬᠤ ᠪᠢ) 19. (12 ᠬᠤ ᠪᠢ) ᠪᠤᠳ ᠤ᠃ (1) 𝑎 2 𝑏 4 ∙(− 12 𝑎𝑏 ) 2 + 14 𝑎 ∙(− 2𝑎 𝑏 2 ) 3 (2) ( 2y − x) (x + 2y )− 2( x+ 2y ) 2 ᠤᠨᠳᠠ ᠬᠤ ᠦᠷ ᠦᠭᠡ ᠤᠨᠳᠠ ᠬᠤ ᠦᠷ ᠦᠭᠡ (3) [2 (𝑥 + 1) 2− (𝑥 + 2) (1 − 2𝑥 )] ÷ (− 32 𝑥 ) (4) ᠦᠷᠡᠵ ᠢᠬᠦᠯᠬ ᠦ ᠦᠢ ᠯᠡᠳᠦᠯ ᠦ ᠲ ᠤᠵᠢᠶ ᠠ ᠪᠠ ᠷ ᠪᠤ ᠳᠤ᠄ (𝑎 − b− 3) (𝑎 − b+ 3) 20. (8 ᠬᠤ ᠪᠢ) ᠦᠷᠡ ᠵᠢᠭᠳ ᠡᠬᠦ ᠪᠤᠯ ᠭᠠ ᠵᠠᠳ ᠠᠯ᠃ (1) 9𝑎 2(𝑥 − 𝑦) + 4𝑏 2(𝑦 − 𝑥) (2) 4 𝑎( 𝑏− 𝑎) − 𝑏 2 21. (10 ᠬᠤᠪ ᠢ) ᠦᠭ ᠬᠦᠭᠳ ᠡᠭᠰᠡ ᠨᠢ 𝑎 𝑚 = 12 𝑥 + 2𝑦 , 𝑎 𝑚 +1 = 14 𝑥 2 +4 𝑦 2 − 𝑥𝑦 ᠪᠣ ᠯ᠂ 𝑎 2 𝑚 +1 ᠢᠢ ᠡᠡᠵᠵ ᠢᠭᠳᠡᠯ ᠣ ᠯ᠃ 22. ( 12 ᠬᠤ ᠪᠢ) ᠤᠷ ᠢᠳᠠᠪᠠ ᠷ ᠡᠢ ᠯᠪᠠᠷᠴᠢ ᠯᠠᠵᠤ ᠳᠠᠷᠠ ᠭ ᠠ ᠨ ᠢ ᠡᠡᠵ ᠵᠢᠭᠳ ᠡᠯ ᠨ ᠢ ᠣ ᠯ᠃ [(𝑎 − 2𝑏 ) 2 − (2 𝑏− 𝑎) (𝑎 + 2𝑏 )− 2𝑎 (2 𝑎− 𝑏) ]÷ 2𝑎 , ᠡᠬᠦ ᠳᠦ 𝑎+ 𝑏= −2 23 .(12 ᠬᠤ ᠪᠢ) ᠤ ᠯᠵᠣ ᠮᠡᠳᠡᠭ ᠰᠡ ᠨᠢ᠄ ᠳᠤ ᠷ ᠠ ᠢ ᠢ ᠳᠠᠷᠠᠭᠠᠯ ᠠᠭᠰᠠ ᠲᠠᠪ ᠤ ᠪᠦᠬᠦ ᠯᠢ ᠲ ᠤᠭᠠ ᠤ ᠺᠦᠸᠠᠳ᠋ ᠤ ᠨ ᠡᠢᠯᠡᠪ ᠦᠷᠢ ᠨ ᠢ 5 ᠢᠢ ᠳᠠᠬ ᠢ ᠲ ᠣᠭ ᠠ ᠪᠣᠯ ᠣᠨ ᠠ ᠃ ᠰᠢᠯ ᠭᠠ ᠪᠠᠳ ᠤᠯᠠᠪᠠ ᠯ ᠄ (1 ) ( −1 ) 2 + 0 2 + 1 2 + 2 2 + 3 2 ᠦ ᠳᠦ᠋ᠩ ᠨᠢ 5 ᠢ ᠢ ᠡ ᠡᠳᠦᠢ ᠳᠠᠬᠢ ᠪᠤ ᠢ ︖ (2) ᠡᠡᠷᠪᠡ ᠳᠠᠷᠠᠭᠠᠯ ᠠᠭᠰᠠ ᠲᠠᠪ ᠤ ᠪᠦᠬᠦ ᠯᠢ ᠲ ᠤᠭᠠ ᠤ ᠳᠤ ᠵᠳᠠᠬ ᠢ ᠲ ᠣᠭ ᠠ ᠨᠢ 𝑛 ᠪᠣᠯ ᠲᠡᠳ ᠡᠭᠡᠷ ᠦ ᠺᠦᠸᠠᠳ᠋ ᠤ ᠨ ᠡᠢᠯᠡᠪ ᠦᠷᠢ ᠢᠢ ᠨ ᠢ ᠪᠢᠴ ᠢᠵᠤ᠂ 5 ᠢᠢ ᠳᠠᠬ ᠢ ᠲᠣᠭ ᠠ ᠪᠣ ᠯᠬᠤ ᠢᠢ ᠲ ᠤᠳᠤᠷᠬ ᠠᠢᠯᠠ᠃ ᠦᠷᠭᠡᠳ ᠭᠡᠯ᠄ ᠳᠤ ᠷ ᠠ ᠢ ᠢ ᠳᠠᠷ ᠠᠭᠠᠯ ᠠᠭᠰᠠ ᠭᠤ ᠷᠪᠠ ᠪᠦᠬ ᠦᠯᠢ ᠲᠤᠭᠠ ᠤ ᠺᠦ ᠸᠠᠳ᠋ ᠤ ᠨᠡᠢ ᠯᠡᠪᠦᠷᠢ ᠨᠢ 3 ᠳᠤ ᠪᠦᠬᠦ ᠯᠢ ᠪᠡᠷ ᠬᠤᠪᠢ ᠶᠠᠭᠳ ᠠᠨ ᠠ ᠦᠦ ︖ ᠡᠡᠷᠪᠡ ᠬᠤ ᠪᠢᠶᠠᠭᠳ ᠠᠬᠤ ᠦᠭᠡᠢ ᠪᠣᠯ ᠦᠯ ᠡᠳᠡᠪᠦ ᠷᠢ ᠨ ᠢ ᠡᠡᠳ ᠦᠢ ︖ ᠴ ᠢᠨᠤ ᠳᠦ᠋ᠩ ᠨᠡᠯᠲᠡ ᠪ ᠡ ᠪᠢᠴ ᠢᠵᠤ ᠰᠢᠯᠲ ᠠᠭᠠ ᠢᠶᠠ ᠲᠤ ᠳᠤᠷᠬᠠᠢ ᠯᠠ᠃ 24. (12 ᠬᠤ ᠪᠢ) ᠵᠢᠷᠤᠭ ᠲᠤ ᠦᠵᠡᠬ ᠦᠯᠦᠭᠰᠡ ᠮᠡᠳ ᠤ᠂ ᠲᠠᠯ ᠠ ᠢᠢ ᠤ ᠷᠲᠤ ᠨᠢ 𝑎 + 𝑏 ᠪ ᠣᠯᠬᠤ ᠲᠡᠭᠰ ᠢ ᠳᠦ᠋ ᠷᠪᠡᠯ ᠵᠢ ᠳᠦ᠋ ᠷᠪᠡ ᠡᠡᠰ ᠡᠭ ᠪ ᠣᠯᠭᠠ ᠬᠤ ᠪᠢᠶᠠᠨ ᠠ᠃ (ᠬ ᠤᠶᠠᠷ ᠲᠡᠭᠰ ᠢ ᠳᠦ᠋ ᠷᠪᠡᠯ ᠵᠢ ᠪᠠ ᠬᠤᠶ ᠠᠷ ᠤ ᠷᠲᠤ ᠳᠦ᠋ ᠷᠪᠡᠯ ᠵᠢ ) (1) ᠵ ᠢᠷᠤᠭ ᠦᠨᠳ ᠦᠰᠦᠯ ᠡ ᠬ ᠤᠶᠠᠷ ᠵᠦ᠋ᠢ ᠯ ᠦ ᠠᠷᠭ ᠠ ᠪᠠ ᠷ ᠲ ᠤᠰ ᠵᠢᠷᠤᠭ ᠤ ᠶᠡᠷᠦ ᠩᠭᠡᠢ ᠲᠠᠯ ᠠᠪᠠᠢ ᠢᠢ ᠣᠯ᠃ (𝑎 ,𝑏 ᠠ ᠭᠤᠯᠤ ᠭᠰᠠ ᠢᠯ ᠡᠷᠬᠡᠢ ᠯᠡᠯ ᠢ ᠶᠡᠷ ᠢᠯᠡᠷᠬ ᠡᠢᠯᠡ᠃ ) (2) ᠡᠡᠷᠪᠡ ᠵᠢᠷᠤᠭ ᠳᠡᠬ ᠢ 𝑎 ,𝑏 (𝑎 𝑏) ᠨᠢ 𝑎 2+ 𝑏 2 = 57 ,𝑎𝑏 = 12 ᠬᠠᠩᠭᠠ ᠪᠠᠯ 𝑎+ 𝑏 ᠢᠢ ᠡ ᠡᠵᠵᠢᠭ ᠳᠡᠯ ᠣ ᠯ᠃ (3) ᠦᠭ ᠬᠦᠭᠳ ᠡᠭᠰᠡ ᠨ ᠢ ( 5+ 2𝑥 ) 2 + (2 𝑥+ 3) 2= 60 ᠂ ᠣᠯᠬᠤ ᠨᠢ (5 𝑥+ 2𝑥 )(2 𝑥+ 3) ᠢ ᠢ ᠡ ᠡᠵᠵᠢᠭ ᠳᠡᠯ᠃ 𝑎 𝑎 𝑏 𝑏