M uhammad al-Xorazmiy nomidagi Toshkent axborot texnologiyalari universiteti

Oddiy giperbolik holat A = C = 0; B≠ 0

A = C = 0 asl tenglama kamayadi Bxy + Dx + Ey + F = 0, shunday:
Bxy + Dx + Ey + F=0
0
Bxy + Dx + Ey=-F
B²xy + BDx + BEy=-BF
B²xy + BDx + BEy + DE=DE - BF
(Bx + E) (By + D)=DE - BF
Ikkita holat mavjud: DE-BF = 0 (parallel ikkita chiziq x va y o'qlar navbati bilan) va DE - ≠ 0 BAT (asimptotlari parallel bo'lgan giperbola x va y o'qlar).
Birinchi holda, qavslardan biri nolga teng bo'lganda, ya'ni echimlarga ega bo'lishning zaruriy sharti paydo bo'ladi., Bx + E = 0 yoki Tomonidan + D = 0. Beri B. B. 0, bizda echimlar mavjud:
, y = har qanday butun son (agar E ning ko'paytmasi B)
x = har qanday butun son, y = - 
(Agar D ning ko'paytmasi B)
Ikkinchi holda x va y qiymatlari DE - BF ning barcha bo'linuvchilarini topish orqali topiladi. Ruxsat bering d ₁, d ₂,..., d _n ning bo'luvchilar to'plami bo'lishi DE-BF. Keyin,


2-misol: 2xy + 5x + 56y + 7 = 0 ni yeching.
Bu holda de - BF bo'linuvchilari = 5*56 - 2*7 = 266 bor: ±1, ±2, ±7, ±14, ±19, ±38, ±133, ±266.
(2x + 56) (2y + 5) = 266 biz olamiz:

• 
  d₁ = 1: x = (1-56)/2 = -55/2, y = (266/1-5)/2 = 261/2
  
• 
  d₂ = -1: x = (-1-56)/2 = -57/2, y=[266/(-1)-5]/2 = 271/2
  
• 
  d₃ = 2: x = (2-56)/2 = -27, y = (266/2-5)/2 = 64
  
• 
  d₄ = -2: x = (-2-56)/2 = -29, y = [266/(-2)-5]/2 = -69
  
• 
  d₅ = 7: x = (7-56)/2 = -49/2, y = (266/7-5)/2 = 33/2
  
• 
  d₆ = -7: x = (-7-56)/2 = -63/2, y = [266/(-7)-5]/2 = -43/2
  
• 
  d₇ = 14: x = (14-56)/2 = -21, y = (266/14-5)/2 = 7
  
• 
  d₈ = -14: x = (-14-56)/2 = -35, y = [266/(-14)-5]/2 = -12
  
• 
  d₉ = 19: x = (19-56)/2 = -37/2, y = (266/19-5)/2 = 9/2
  
• 
  d₁₀ = -19: x = (-19-56)/2 = -75/2, y = [266/(-19)-5]/2 = -19/2
  
• 
  d₁₁ = 38: x = (38-56)/2 = -9, y = (266/38-5)/2 = 1
  
• 
  d₁₂ = -38: x = (-38-56)/2 = -47, y = [266/(-38)-5]/2 = -6
  
• 
  d₁₃ = 133: x = (133-56)/2 = 77/2, y = (266/133-5)/2 = -3/2
  
• 
  d₁₄ = -133: x = (-133-56)/2 = -189/2, y = [266/(-133)-5]/2 = -7/2
  
• 
  d₁₅ = 266: x = (266-56)/2 = 105, y = (266/266-5)/2 = -2
  
• 
  d₁₆ = -266: x = (-266-56)/2 = -161, y = [266/(-266)-5]/2 = -3
  

So'ralgan tenglamalarning faqat 8 ta echimi yuqorida qizil rang bilan belgilangan.