Matematika - o'rta bosqich
Тематический план
-
- Etakchi o'quvchilar ro'yhatiТекущая тема
Etakchi o'quvchilar ro'yhati
- Aziz Ilhomov
- Yunusbek Sotiboldiev
- Artyom Sergeev
- Ravshat Ollayorov
- Sherzod Usmonov
- Videodarslar
- I tur masalalari
I tur masalalari
Agar \( x, y \) haqiqiy sonlar bo’lsa \( 2^x + 2^\frac{2-x-y}{2} + 2^y \) ifodaning eng kichik qiymatini toping. Tenglik qaysi hollarda bajariladi?
\( ABC \) uchburchakda \( r \) ichki chizilgan aylana radiusi, \( r_a \) \( BC \) tomoniga va \( AC, AB \) tomonlari davomiga urinadigan aylana radiusi bo’lsin.
U holda \( \frac{r}{r_a} = \frac{p-a}{p} \) tenglikni isbotlang, bu yerda \( p \) yarim perimeter.
- \( \frac{(x^2+1)(x+1)^2 + x^2}{x^2(x^2+1)+1} = x + \frac{1}{x} \) tenglamani eching.
- \( x^3 - y^3 = xy + 61 \) tenglamani natural sonlarda yeching.
\( ABCD \) qavariq to’rtburchakda \( \angle BCD = 90^ \circ \) va \( E \) nuqta \( AB \) ning o’rtasi bo’lsa, \( \frac{AD+BD}{EC} \geq 2 \) ni isbotlang.
- II tur masalalari
II tur masalalari
- \( 61 \cdot 79 \cdot 107 + 72 \cdot 90 \cdot 44 \) son murakkab son bolishini isbotlang.
- \( x^3+y^3 = x - y \) shartni qanoatlantiradigan musbat \( x, y \) sonlar uchun \( x^2 +4y^2 < 1 \) tengsizlikni isbotlang.
- Tomonlari \( 3, 5, 7, 4 \) ga teng, diagonallari esa o’zaro perpendikulyar bo’lgan qavariq to’rtburchak mavjudmi? Javobingizni asoslab bering.
- \( ABC \) uchburchakda \( A_1, B_1, C_1 \) nuqtalar mos ravishda \( BC, AC, AB \) tomonlarning o’rtalari bo’lsin. Ma’lumki, \( A_1A \) va \( B_1B - A_1B_1C_1 \) uchburchak bissektrisalari. \( ABC \) uchburchakda barcha burchaklar topilsin .
- Tenglamalar sistemasini yeching: \( x^2 + y^3 = 3 \sqrt{2} \brace x^6 + y = 3 \sqrt{2} \)
- III tur masalalari
III tur masalalari
\( p, p+2 \) va \( p+10 \) sonlari tub bo‘ladigan barcha \( p \) natural sonlarni toping.
\( ABC \) uchburchakda \( \angle A = \alpha, \angle B = \beta \) bo‘lib \( 3 \sin \alpha + 4 \cos \beta = 6 \) va \( 4 \sin \beta+ 3 \cos \alpha= 1 \) tengliklar o‘rinli bo‘lsa, \( \angle C \) ni toping.
\( ABC \) uchburchakda \( BC \) va \( AC \) tomonlardan mos ravishda \( D \) va \( E \) nuqtalar olingan.
Agar \( AB=AC, \angle BAD = 30^ \circ, AE=AD \) tengliklar o‘rinli bo‘lsa, u holda \( \angle CDE \) ni toping.
Ushbu \( \frac{a^2+2019}{2025} \) kasr butun bo‘ladigan barcha natural \( a \) sonlarini toping.
Manfiy bo‘lmagan \( x, y, z \) sonlari uchun
\( x+[y]+ \{ z \} = 13,2 \)
\( [x]+\{ y \}+ z = 14,3 \)
\( \{ x \} +y+ [z] = 15,1 \)
tengliklar sistemasi o‘rinli bo‘lsa, u holda \( x \) ni toping. Bu yerda \( [x] \) soni \( x \) ning butun qismi, \( \{ x \} \) esa \( x \) ning kasr qismi.
- Masalalarni echilish namunalari
- Boshqa kurslar