Bilimlar bellashuvi va olimpiadalar

Olimpiada IX tur yechimlari ( 8-sinf)

Siz bu yerda saytimizda muntazam chop etilib kelinayotgan matematika fanidan 8-sinf o’quvchilariga mo’ljallangan «Olimpiada IX tur» masalalari yechimlari va izohlari bilan tanishishingiz mumkin.

Yechimlar:

1) Yechish:   xy≠ 0 deb tenglikni ikkala tomonini kvadratga oshiramiz.

(x3-y3)2= 4x2y2,   (x3-y3)2 +4x3y3= 4x2y2+4x3y3, (x3-y3)2= 4x2y2(1+xy), bu yerdan

2) Javob: 324.

3) Yechish:

(6x2-7x)2-2(6x2-7x)-3=0, 6x2-7x= y belgilash kiritamiz, unda tenglama y2-2y-3=0 ko’rinishga keladi.Bu tenglamani yechsak y1=3, y2=-1.O’rniga qo’ysak, 6x2-7x-3=0 va 6x2-7x+1=0 tenglamalar hosil bo’ladi. Bularni yechsak.

J: x1=1,5 ;   

4) Yechish:

x2+3x+m=0 , x1-x2=6, x1= 6+x2.

x1+x2= -3,  6+x2+x2=- 3, 2x2= -9; x2= -4,5.

x1= -3-x2= -3-(-4,5) = -3+4,5= 1,5.

m=x1x2= 1,5⋅ (-4,5)= – 6,75;           Javob: m= – 6,75.

5) Yechish:

Javob: (1;2), (2;1)

6) Yechish:

Shartga ko’ra sistema tuzamiz:        sistemani yechsak, x=6, y= 54;

Javob: Kichigi 6 kattasi 54.

7)  Intervallar usuli bilan yechsak

 

8) Yechish:

Sistemani 1-tengsizligini soddalashtirsak  ga , 2-si esa  ga ega.Buni intervallar usuli bilan yechsak, x<-2, 0<x<2 va kesma bilan kesishmasini olsak Javob:

9) Yechish:

ACBM parallelogramda shartga ko’ra  va <ECF=600, u holda <ACE= 300.Demak, AE=0,5AC= 8 m.AEC uchburchakdan AC= 16m, AE= 8m,  CE2= AC2-AE2, yoki

10)Tengsizlikninh ikkala tomoni ham musbat, u holda ikkala tomonini kvadratga oshirsak buni yechsak,

Muallif haqida

Foziljon Anapiyayev

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

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