) Uchburchak ikkita tomonining uzunliklari 6 sm va 3 sm ekanligi ma’lum. Agar berilgan tomonlarga tushirilgan balandliklar yig’indisining yarmi uchinchi balandlikka teng bo’lsa, uchburchakning uchinchi tomoni necha sm.

Quyida keltirilgan tengliklardan qaysilari ayniyat emas? 1) \((x + a) \cdot (x - b) = {x^2} - (a - b)x - ab;\) 2) \((x - c) \cdot (x - d) = {x^2} + (c - d)x + cd;\) 3) \((x - c) \cdot (x + d) = {x^2} - (c - d)x - cd;\) 4) \(\begin{array}{l}6ab + (2{a^3} + {b^3} - (3a{b^2} - ({a^3} + 2a{b^2} - \\ - {b^3}))) = 3{a^3} - a{b^2} + 6ab;\end{array}\) 5) \(\begin{array}{l}5{a^2} - 3{b^2} - (({a^2} - 2ab - {b^2}) - (5{a^2} - 2ab - \\ - {b^2})) = 9{a^2} + 4ab - 3{b^2}.\end{array}\)

\(\sqrt[n]{{16 \cdot \sqrt[n]{{16 \cdot \sqrt[n]{{16...}}}}}} = m\) bo’lsin, m va n musbat butun sonlar bo’lsa, m-n ni toping.

\(\frac{{({{8,7}^2} - {{11,3}^2})({{13,3}^2} - {{12,3}^2})}}{{({{4,2}^2} - {{5,8}^2})({{2,3}^2} - {{0,3}^2})}}\) ni hisoblang.

\(\left| {\frac{1}{{1,5 - \frac{x}{2}}}} \right| > \frac{4}{{15}}\)tengsizlikning barcha butun sonlardagi yechimlari yig’indisini toping.

Agar \(3 \le x \le y \le z \le t \le 27\) bo’lsa, \(\frac{x}{y} + \frac{z}{t}\) ifodaning eng kichik qiymatini toping.

) Teng yonli to’g’ri burchakli uchburchakka ichki chizilgan aylana radiusining uchburchak gipotenuzasiga o’tkazilgan balandlikka bo’lgan nisbatini toping.

Arifmetik progressiya uchinchi va to’qqizinchi hadlarining yig’indisi 10 ga teng. Shu progressiyaning dastlabki 11 ta hadlari yig’indisini toping.

) \(\sin {18^0}\sin {54^0} = ?\)

To’gri burchakli ABC uchburchakda C burchak to’g’ri burchak bo’lib, AN bissektrisa va AB gipotenuzada D nuqta olingan bo’lib, AD=2 va \({S_{\Delta ANC}}:{S_{\Delta AND}} = 3\) bo’lsa, AC=?

\(\begin{array}{l}\sin {10^0}\sin {20^0}\sin {30^0}\sin {40^0}\sin {50^0} \cdot \\ \cdot \sin {60^0}\sin {70^0}\sin {80^0} = ?.\end{array}\)

\({\left( {3\frac{3}{8}} \right)^{ - \frac{2}{3}}} + {27^{\frac{2}{3}}} \cdot {9^{0,5}} \cdot {3^{ - 2}} + {\left( {{{\left( {\frac{7}{9}} \right)}^3}} \right)^0} - {\left( { - \frac{1}{2}} \right)^{ - 2}}\) ni hisoblang.

) Uchburchakning 6 ga teng balandligi uning asosi uzunligini 7:18 kabi nisbatda bo’ladi. Shu balandlikka parallel va uchburchakning yuzini teng ikkiga bo’ladigan to’g’ri chiziq kesmasining uzunligini toping.

\(\frac{{{3^9} \cdot {2^{19}} + 15 \cdot {4^9} \cdot {9^4}}}{{{6^9} \cdot {2^{10}} + {{12}^{10}}}} \cdot {\left( {1\frac{1}{2}} \right)^{ - 1}}\) ni hisoblang.

Ishlab chiqarish samaradorligi birinchi yili 15% ga, ikkinchi yili 16% ga ortdi. Shu ikki yil ichida samaradorlik necha % ga ortgan?

\(\frac{{\cos 2x}}{{\frac{{\sqrt 2 }}{2} + \sin x}} = 0\) tenglamaning \(\left[ {0;6\pi } \right]\) kesmada nechta ildizi bor?

Parallelogrammning perimetri 40 sm, uning balandliklari 2:3 kabi nisbatda bo’lsa, parallelogrammning katta tomonini toping.

m ning qanday qiymatlarida \(\left\{ {\begin{array}{*{20}{c}}{2x - y = 3m - 4}\\{x - y = m - 1}\end{array}} \right.\)tenglamalar sistemasining yechimi koordinata tekisligining IV choragiga tegishli bo’ladi.

\(y = \frac{{{x^2} + ax + b}}{{{x^2}}}\) egri chiziq A(-3;0) nuqtada x o’qiga urinsa, a+b=?

\(a,b \in N\) va \(b = \frac{{a + 3}}{4} + \frac{{a + 3}}{5}\) bo’lsa, a eng kamida nechaga teng?

P(x) ning (x-3)2 ga bo’linmasidan qolgan qoldiq (2x-3) bo’lsa, (x-3) ga bo’linmasidan qolgan qoldiqni toping.

\({\log _2}25\)ning butun qismini toping.

a bilan b ning o’rta arifmetigi va o’rta geometrigi 4 bo’lsa, a-1 bilan b-1 ning o’rta geometrigi topilsin.

y=9 – 0,5x funksiyaning qiymatlar sohasini toping. A) \(\left( {9;\infty } \right)\)

ABC tomoni 16 sm bo’lgan teng tomonli uchburchak. \(\left[ {BH} \right] \bot \left[ {AC} \right],\left[ {HK} \right] \bot \left[ {BC} \right],\) \(\left[ {KT} \right] \bot \left[ {BH} \right]\) bo’lsa, \({S_{\Delta THK}}\)necha sm2?

) To’g’ri burchakli uchburchakning balandligi gipotenuzani 3 va 12 ga teng kesmalarga ajratsa, shu balandlikni toping.

) \(\sqrt {a + \sqrt {a + \sqrt {a + ...} } } = 4\) tenglikdan a ni toping.

\(\arccos \frac{{36}}{{85}} - \arccos \frac{{15}}{{17}} = ?\)

Bir bola bilyard sharchalarini 9 tadan to’plarga ajratganda 5 ta, 12 tadan ajratganda 8 ta, 14 tadan ajratganda 10 ta sharcha yetmayapti. Bunga ko’ra bolada kamida nechta sharcha mavjud?

\({\log _{\sqrt 5 }}\sqrt {5 \cdot \sqrt {5 \cdot \sqrt {5 \cdot ...} } } = ?\)