Ko‘rsatkichli tengsizliklar mavzusidan test savollari
Tenglamaning kata ildizini toping:
3^{5-2x^{2}}-4\cdot 3^{-x^{2}-5}=-3^{-14}
\begin{cases}3^{3x-1}+4^{y}=21 \\ -27^{2x}+2^{2y}=11 \end{cases} bo‘lsa, x ga teskari sonni toping.
\begin{cases}{3^{2x-y}=\sqrt[3]{27^{2}}} \\ {9^{x}\cdot 9^{y}=3^{14}} \end{cases} tenglamani qanoatlantiruvchi barcha x va y larning yig‘indisini toping.
\begin{cases}3^{m}+2\cdot 4^{n+1}=17 \\ 4^{n}-5\cdot 3^{m}=-44 \end{cases} bo‘lsa,
m+n=?
Tengsizlikni yeching:
(\frac{1}{3})^{x^{2}+2x}+(\frac{1}{3})^{x^{2}+2x-2}>\frac{10}{27}
(4^{\sqrt{x-6}}-1)(3\cdot 2^{x}-96)<0 tengsizlikni yeching.
(4^{\sqrt{x-6}}-1)(3\cdot 2^{x}-96)\ge 0 tengsizlikni qanoatlantiruvchi eng kichik natural sonni toping.
Tengsizlikni yeching:
(\sqrt{\pi }-1)^{\ln (2sinx)}\ge 1;x\in[0;2\pi ]
0.(3)^{12-5x}<27 tengsizlikning nechta natural yechimi mavjud
Tengsizlik x ning nechta butun qiymatida o‘rinli?
4\cdot (0.2)^{x^{2}+x-2}-15\cdot (0.2)^{x^{2}+x-1}\ge 1
Quyidagi tenglamaning ildizlari nisbatini toping:
(\sqrt{2+\sqrt{3}})^{x}+(\sqrt{2-\sqrt{3}})^{x}=4
25<3^{2x-3}<90 tensizlikni qanoatlantiruvchi nechta butun son mavjud?
Tengsizlikni yeching:
(\frac{1}{3})^{5-2x}\ge 27
(x+2)^{\log_{2}(x^{2}+1)}<(x+2)^{\log_{2}(2x+9)}
8<3^{2x-3}<90 tensizlikni qanoatlantiruvchi nechta butun son mavjud?
Tengsizlik x ning nechta butun qiymatida o‘rinli:
(0.5)^{x^{2}-x-4}-3\cdot (0.5)^{x^{2}-x-2}>1
30<3^{2x+5}<70 tensizlikni qanoatlantiruvchi nechta butun son mavjud?
Tengsizlikni yeching:
(\frac{\pi }{2}-\frac{e}{3})^{\ln (2cosx)}\ge 1 x\in[0;2\pi ]
Tengsizlikni yeching (\frac{4}{5})^{\sin ^{2}x}\cdot (\frac{25}{16})^{cosx}<2^{2}\cdot 5^{-1}
Quyidagi tenglama nechta ildizga ega?
3^{x}=x^{2}+3
Tengsizlik x ning nechta butun qiymatida o‘rinli?
2^{x^{2}-x-6}+3\cdot 2^{x^{2}-x-4}>13
(x-2)^{x^{2}-6}>(x-2)^{10} tengsizlikni yeching.
Quyidagi sonlardan qaysilari birdan kata?
1) 0.2^{x}\cdot 5^{y}x>1 va y<0;
2) 0.75^{x}\cdot 1.(3)^{y}x<0 va y>0;
3) 0.4^{x}\cdot 2.5^{y}x>y>0;
4) 0.(3)^{x}\cdot 3^{y}x<y<0;
5) 0.8^{x}\cdot 1.25^{x}x>1
18<5^{x-2}<4012 tengsizlikni qanoatlantiruvchi butun sonlar yig‘indisini toping.
Quyidagi tengsizlik nechta natural ildizga ega?
(\frac{25}{49})^{x-10}\ge (\frac{7}{5})^{2x-10}