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 an=74 bu arifmetik progressiyaning hadi bo’lsa, u holda an= 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 x1,2=± 2, y1,2=± 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.