Olimpiada VIII tur yechimlari (9-sinf)

Siz bu yerda saytimizda muntazam chop etilib kelinayotgan matematika fanidan 9-sinf o’quvchilariga mo’ljallangan «Olimpiada VIII tur» masalalari yechimlari va izohlari bilan tanishishingiz mumkin.

Javoblar:

1) Yechish:

     Javob: -3,5.

2) Yechish:

D= b²-4ac= 0, yoki 9-4 2 (17+m)=0, buni yechsak 9-8(17+m)=0;  ;

3) Yechish:

Javob: p>n.

4) Yechish:

100000-100000:100⋅ 30= 100000-30000= 70000;

70000-70000:100⋅ 30= 70000-21000= 49000;            Javob: 49000 so’m.

5) Yechish:

Shartga ko’ra a₁=4;  d=4; Agar a_n=74 bu arifmetik progressiyaning hadi bo’lsa, u holda a_n= a₁+(n-1)d yoki

74=4+(n-1)⋅ 4, bundan n= 21,5.Javob: hadi emas.

6) x²-2ax+a²-1=0;   Shartga ko’ra 3²-2a 3+a²-1=0;  a²-6a+8=0; Buni yechsak,

a₁=2; a₂=4;       Javob: a₁=2; a₂=4.

7) Javob: n=3.

8) Yechish:

bu yerda x,y≠ 0. 1-tenglamani 2-tenglamaga bo’lsak  yoki x²= 4y², x=± 2y.

Ikkita sistemaga egamiz:

1) dan x_1,2=±  2, y_1,2=± 1.

2) sistema yechimga ega emas.Javob: (-2;-1) va (2;1).

9)  Javob:

10) Yangi o’zgaruvchi kiritamiz:  u holda  yoki

Buni yechsak , 1<y<4 yoki Bundan 1<x<16, Javob: x=15.