Siz bu yerda 7-sinf matematika fanidan «Olimpiada III tur masalalari» yechimlari bilan tanishishingiz mumkin.
1.Yechish:
xy-x-y-4=0; xy-x-y+1-5=0; y(x-1) –(x-1)=5; (x-1)(y-1)= 5;
5= 5⋅1=1⋅5=(-5)⋅(-1)=(-1)⋅(-5) U holda,
1) x-1=5 2) x-1=1 1) x-1= -5 1) x-1= -1
y-1=1 y-1=5 y-1= -1 y-1= -5
Bulardan: (6;2), (2;6) , (-4;0), (0; -4) juftliklarni topamiz. Javob: (6;2), (2;6) , (-4;0), (0; -4)
2.Yechish:
Hammasi bo’lib 
ta o’yin o’ynalgan. Agar hamma o’yin biron komandani g’alabasi bilan tugaganda edi, 21 ⋅3= 63 ochko yig’ilgan bo’lar edi.Masalaning shartidan jami 58 ochko yig’ilgan.Durangga 1 ochko berilgani uchun 63-58=5 ta o’yin durang bo’lgan. Javob: 5 ta
3.Yechish:
x8 + x4 +1 = (x4+1)2-x4= (x4+1-x2)(x4+1+x2)= (x4-x2+1)(x2-x+1)(x2+x+1).
4.Yechish:
tenglikdan foydalansak,
=
;
5.Yechish:
x- qarg’alar soni, y-shohlar soni bo’lsin.U holda shartga binoan 5y+1=x va 6(y-1)=x
5y+1= 6(y-1); Bundan y= 7.Demak x= 5 +1= 36; Javob: 36 ta qarg’a, 7 ta shoh
