Bilimlar bellashuvi va olimpiadalar

Olimpiada III tur masalalar yechimlari (7-sinf)

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

Muallif haqida

Foziljon Anapiyayev

Andijon viloyati, Baliqchi tumani.
O‘zbekiston xalq ta’limi a’lochisi
Xozirda nafaqada.

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