Tengsizliklar sistemasining eng katta butun yechimini ko’rsating.\(\left\{ {\begin{array}{*{20}{c}}{\frac{{x + 5}}{4} - 2x \ge 0}\\{x - \frac{{2x - 8}}{5} \ge 1 - 2x}\end{array}} \right.\)

\(y = \sqrt {\frac{{4 - \sqrt {17} }}{{3 - 2x}}} \) funksiyaning aniqlanish sohasini toping.

. Funksiyaning aniqlanish sohasini toping \(y = \sqrt {\frac{{\left( {x - 2} \right)\left( {5 - x} \right)}}{{\left( {x - 3} \right)\left( {x - 4} \right)}}} \)

Tengsizlikni yeching \({x^2} - x + 1 > 0\)

Tengsizlikning manfiy butun yechimlari yig’indisini toping \(\frac{{\left( {x - 5} \right)\left( {x + 3} \right)}}{{{{\left( {x + 1} \right)}^2}}} \le 0\)

Ushbu \(\left( {{x^2} - x - 1} \right)\left( {{x^2} - x - 7} \right) \le - 5\) tengsizlikning eng katta butun va eng kichik butun yechimlari ayirmasini toping.

\(8 + \frac{{6x - 8}}{{10}} > \frac{{x - 2}}{6} + \frac{{1 - 5x}}{8} + \frac{1}{4}\) tengsizlikni qanoatlantiruvchi eng kichik butun manfiy son nechaga teng?

Agar \(5 \le x \le y \le z \le t \le 320\) bo’lsa, \(\frac{x}{y} + \frac{z}{t}\) ifodaning eng kichik qiymatini toping.

Agar \(f = \frac{1}{{1 - {x^2}}}\) bo’lsa, \(f\left( {f\left( x \right)} \right) \le 0\) tengsizlikning butun sonlardan iborat nechta yechimi bor?

. Nechta tub son \({x^2} - 50 > 0\) tengsizlikning yechimi bo’la olmaydi?

m ning qanday qiymatida \(\frac{{mx + 9}}{x} \ge - 10\) tengsizlikning eng katta manfiy echimi -3 ga teng bo’ladi?

Agar \( - 2 < a < - 1\;va - 3 < b < - 2.5\) bo’lsa, \(a - b\) ayirma qaysi sonlar orasida bo’ladi?

Ushbu \(y = \frac{{\sqrt {x + 1} + \sqrt {x - 2} }}{{\sqrt {x - 3} - \sqrt {5 - x} }}\) funksiyaning aniqlanish sohasiga tegishli barcha butun sonlarning yig’indisini toping.

. \(y = \frac{{\sqrt {{x^2} - x - 30} }}{{\sqrt {\left| {{x^2} - x - 42} \right|} }}\) funksiyaning aniqlanish sohasini toping.

n ning 10 dan oshmaydigan nechta natural qiymatida \(n{x^2} + 4x > 1 - 3n\) tengsizlik x ning ixtiyoriy qiymatida o’rinli?

Tengsizlikni yeching \(9{x^2} - 6x + 1 > 0\)

agar \(\frac{1}{a} < - 1\) bo’lsa quyidagi ifodalardan qaysi birining qiymati eng katta bo’ladi?

\(x\left( {x + 1} \right)\left( {x + 2} \right)\left( {x + 3} \right) \le 24\) tengsizlikning yechimlari orasida nechta butun son bor?

Tengsizliklar sistemasini yeching \(\left\{ {\begin{array}{*{20}{c}}{x\left( {x + 1} \right) + 10 > {{\left( {x + 1} \right)}^2} + 3}\\{3x - 4\left( {x - 7} \right) \ge 16 - 3x}\end{array}} \right.\)

\({x^2} + px + {q^2} = 0\;\left( {q \ne 0} \right)\) tenglama \(\frac{p}{q}\) ning qanday qiymatlarida haqiqiy ildizlarga ega emas?

Nechta tub son \(3 < \frac{{5x - 1}}{{2x - 3}} < 5\) tengsizlikning yechimi bo’la oladi?

. Tengsizlikning butun yechimlari nechta? \(\frac{{\left( { - {x^2} + x - 1} \right)\left( {{x^2} + x - 2} \right)}}{{{x^2} - 7x + 12}} \ge 0\)

\(\left\{ {\begin{array}{*{20}{c}}{\left( {x + 2} \right)\left( {2 - x} \right) < \left( {x + 3} \right)\left( {4 - x} \right)}\\{\frac{{3 + x}}{4} + \frac{{1 - 2x}}{6} \ge 1}\end{array}} \right.\) tengsizliklar sistemasining butun sonlardan iborat yechimlari nechta?

. Ushbu \(f\left( x \right) = \sqrt {\frac{{2{x^2} + x - 6}}{{2x - 5}}} \) funksiyaning aniqlanish sohasiga tegishli eng kichik natural sonni va funksiyaning shu nuqtadagi qiymatini toping?

. Tenglizlikning barcha butun yechimlari yig’indisini toping. \(\left( {x - 1} \right){\left( {x + 1} \right)^2}{\left( {x - 3} \right)^3}{\left( {x - 4} \right)^4} \le 0\)

Quyidagi tengsizliklarning qaysilari o’zaro teng kuchli? \(1)\frac{{x - 3}}{{x + 1}} \ge 0;\;2)\frac{{x - 3}}{{{x^2} + 1}} \ge 0;\;\;3)\frac{{x - 3}}{{{x^2}}} \ge 0;\;\;4)x - 3 \ge 0\)

Agar a<-1 bo’lsa, quyida keltirilgan ifodalardan qaysi birini qiymati eng katta bo’ladi?

\(\left( {m - 3} \right)\left( {m - 7} \right)\)ifodaning qiymati m ning har qanday qiymatida musbat bo’lishi uchun unga qanday eng kichik butun sonni qo’shish kerak?

Ushbu \(1.\;{a^2} > 0;2.\;{a^2} - 10\left\langle {0;3.{{\left( {a - 5} \right)}^2} \ge 0;4.\;\frac{1}{{{a^2}}} + {a^2}} \right\rangle 2\) tengsizliklarning qaysilari a ning barcha qiymatlarida o’rinli?

\(y = \sqrt[4]{{\frac{{{x^2} - 6x - 16}}{{{x^2} - 12x + 11}}}} + \frac{2}{{{x^2} - 49}}\) funksiyaning aniqlanish sohasini toping.

Agar x va y sonlari uchun munosabat o’rinli bo’lsa, quyidagi tengsizliklardan qaysi biri doimo o’rinli bo’ladi?

. \(\left( {{n^2} - 3} \right)\left( {{n^2} - 21} \right) < 0\) tengsizlikni qanoatlantiruvchi n ning nechta butun qiymati bor?

Sonlarni kamayish tartibida joylashtiring. \(a = \sqrt {101} + \sqrt {103} ;b = \sqrt {99} + \sqrt {105} ;c = 19.9\)

Tengsizliklar sistemasining butun yechimlari yig’indisini toping\(\left\{ {\begin{array}{*{20}{c}}{\frac{{\left( {x + 4} \right)\left( {x - 5} \right)}}{{{{\left( {x - 1} \right)}^2}}} \le 0}\\{x \ge - 6}\end{array}} \right.\)

Ushbu \(\frac{{z - 8}}{{k - 10}} = \frac{k}{z}\) tenglama ildizga ega bo’lmaydigan k ning barcha qiymatlari yig’indisini toping.

. Tengsizlikning eng katta butun manfiy va eng kichik butun musbat yechimlari ko’paytmasini toping. \(\frac{{{x^4} - 3{x^3} + 2{x^2}}}{{30 - {x^2} - x}} < 0\)