\(a,\left(2-x\right)\left(\dfrac{4}{5}-x\right)< 0\)

=>Trong 2 số phải có 1 số âm và 1 số dương

Mà \(2-x>\dfrac{4}{5}-x\)

=>\(\dfrac{4}{5}< x< 2\)

Vậy...

a: \(\left(x-2\right)^2+\left(x-y\right)^6+3\ge3\)

\(\Leftrightarrow A=\dfrac{2003}{\left(x-2\right)^2+\left(x-y\right)^6+3}\le\dfrac{2003}{3}\)

Dấu '=' xảy ra khi x=y=2

b: \(B=-\left(2x+\dfrac{1}{3}\right)^6+3\le3\forall x\)

Dấu '=' xảy ra khi x=-1/6

c: \(C=\dfrac{x^{2016}+2015+2}{x^{2016}+2015}=1+\dfrac{2}{x^{2016}+2015}\le\dfrac{2}{2015}+1=\dfrac{2017}{2015}\)

Dấu '=' xảy ra khi x=0

a) \(\left|x-\dfrac{5}{3}\right|< \dfrac{1}{3}\)

\(\Rightarrow\dfrac{-1}{3}< x-\dfrac{5}{3}< \dfrac{1}{3}\)

\(\Rightarrow\dfrac{-1}{3}+\dfrac{5}{3}< x-\dfrac{5}{3}+\dfrac{5}{3}< \dfrac{1}{3}+\dfrac{5}{3}\)

\(\Rightarrow\dfrac{4}{3}< x< 2\)

b) \(\left|x+\dfrac{11}{2}\right|>\left|-5,5\right|=5,5\)

\(\Rightarrow\left\{{}\begin{matrix}x+\dfrac{11}{2}< 5,5\\x+\dfrac{11}{2}>5,5\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x< 5,5-\dfrac{11}{2}=0\\x>5,5-\dfrac{11}{2}=0\end{matrix}\right.\)

=> Với x khác 0 thì thõa mãn đề bài

c) \(\dfrac{2}{5}< \left|x-\dfrac{7}{5}\right|< \dfrac{3}{5}\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{2}{5}< x-\dfrac{7}{5}< \dfrac{3}{5}\\-\dfrac{2}{5}< x-\dfrac{7}{5}< -\dfrac{3}{5}\end{matrix}\right.\)

Ta thấy trường hợp 2 là trường hợp không thể xảy ra

=> Loại

Vậy \(\dfrac{2}{5}< x-\dfrac{7}{5}< \dfrac{3}{5}\)

\(\Rightarrow\dfrac{2}{5}+\dfrac{7}{5}< x< \dfrac{3}{5}+\dfrac{7}{5}\)

\(\Rightarrow\dfrac{9}{5}< x< 2\) (nhận)

p/s : làm đại nha , ko bik đúng sai

c)

Ta có :\(2+\dfrac{1}{1+\dfrac{1}{2+\dfrac{1}{1+\dfrac{1}{2}}}}\)

\(=2+\dfrac{1}{1+\dfrac{1}{2+\dfrac{1}{\dfrac{3}{2}}}}\) \(=2+\dfrac{1}{1+\dfrac{1}{2+\dfrac{2}{3}}}\) \(=2+\dfrac{1}{1+\dfrac{1}{\dfrac{8}{3}}}\) \(=2+\dfrac{1}{1+\dfrac{3}{8}}\) \(=2+\dfrac{1}{\dfrac{11}{8}}\) \(=2+\dfrac{8}{11}\) \(=\dfrac{30}{11}\)

d) \(\left(\dfrac{1}{3}\right)^{-1}-\left(-\dfrac{6}{7}\right)^0+\left(\dfrac{1}{2}\right)^2:2\)

\(=3-1+\left(\dfrac{1}{2}\right)^2:2\)

\(=3-1+\dfrac{1}{4}:2\)

\(=3-1+\dfrac{1}{8}\)

\(=\dfrac{17}{8}\)

a, \(2^3< 2^x< 2^9.2^{-5}\)

\(2^3< 2^x< 2^4\)

cn lại mk ko bt, hình như đề hơi sai sai

a) \(\left(-1\dfrac{3}{5}+x\right):\dfrac{12}{13}=2\dfrac{1}{6}\)

⇔ \(\left(\dfrac{-8}{5}+x\right).\dfrac{13}{12}=\dfrac{13}{6}\)

⇔ \(-\dfrac{8}{5}+x=\dfrac{13}{6}:\dfrac{13}{12}\)

⇔ \(-\dfrac{8}{5}+x=2\)

⇔ \(x=2+\dfrac{8}{5}\)

⇔ \(x=\dfrac{18}{5}\)

b) \(\dfrac{-4}{7}x+\dfrac{7}{5}=\dfrac{1}{8}:\left(-1\dfrac{2}{3}\right)\)

⇔ \(-\dfrac{4}{7}x+\dfrac{7}{5}=-\dfrac{3}{40}\)

⇔ \(-\dfrac{4}{7}x=-\dfrac{3}{40}-\dfrac{7}{5}\)

⇔ \(-\dfrac{4}{7}x=-\dfrac{59}{40}\)

⇔ \(x=\left(-\dfrac{59}{40}\right):\left(-\dfrac{4}{7}\right)\)

⇔ \(x=\dfrac{413}{160}\)

a, \(\left(-1\dfrac{3}{5}+x\right):\dfrac{12}{13}=2\dfrac{1}{6}\)

=> \(\left(-1\dfrac{3}{5}+x\right):\dfrac{12}{13}=\dfrac{13}{6}\)

=> \(\left(-1\dfrac{3}{5}+x\right)=\dfrac{13}{6}.\dfrac{12}{13}\)

=> \(\left(-1\dfrac{3}{5}+x\right)=2\)

=> \(\dfrac{-8}{5}+x=2\)

=> x= \(2+\dfrac{8}{5}=\dfrac{10}{5}+\dfrac{8}{5}\)

=> x= \(\dfrac{18}{5}\)

Vì /2x+1/ ≥ 0

=> /2x+1/ + 2017 ≥ 2017

=> 2016/ /2x+1/ +2017 ≤ 2016/2017

Vậy Bmax = 2016/2017 khi /2x+1/ = 0 => 2x+1 =0 => 2x=-1

=> x = -1/2

1.

\(\left(\dfrac{-2}{3}\right).0,75+1\dfrac{2}{3}:\left(\dfrac{-4}{9}\right)+\left(\dfrac{-1}{2}\right)^2\)

\(=\left(\dfrac{-2}{3}\right).\dfrac{3}{4}+\dfrac{5}{3}.\left(\dfrac{9}{-4}\right)+\dfrac{1}{4}\)

\(=-\dfrac{1}{2}+\dfrac{45}{-12}+\dfrac{1}{4}\)

\(=-\dfrac{6}{12}+\dfrac{-45}{12}+\dfrac{3}{4}\)

\(=\dfrac{-48}{12}\)

\(=-4\)

2.

a) \(\dfrac{3}{4}-\left(x+\dfrac{1}{2}\right)=\dfrac{4}{5}\)

\(\Leftrightarrow x+\dfrac{1}{2}=\dfrac{3}{4}-\dfrac{4}{5}\)

\(\Leftrightarrow x+\dfrac{1}{2}=\dfrac{-1}{20}\)

\(\Leftrightarrow x=\dfrac{-1}{20}-\dfrac{1}{2}\)

\(\Leftrightarrow x=\dfrac{-1}{20}-\dfrac{10}{20}\)

\(\Leftrightarrow x=\dfrac{-11}{20}\)

b) \(\left|x-\dfrac{2}{5}\right|+\dfrac{3}{4}=\dfrac{11}{4}\)

\(\Leftrightarrow\left|x-\dfrac{2}{5}\right|=\dfrac{11}{4}-\dfrac{3}{4}\)

\(\Leftrightarrow\left|x-\dfrac{2}{5}\right|=2\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{2}{5}=-2\Rightarrow x=-2+\dfrac{2}{5}=\dfrac{-8}{5}\\x-\dfrac{2}{5}=2\Rightarrow x=2+\dfrac{2}{5}=\dfrac{12}{5}\end{matrix}\right.\)

3.

a) \(\dfrac{16}{2^n}=2\)

\(\Leftrightarrow2^n=16:2\)

\(\Leftrightarrow2^n=8\)

\(\Leftrightarrow2^n=2^3\)

\(\Leftrightarrow n=3\)

b) \(\dfrac{\left(-3\right)^n}{81}=-27\)

\(\Leftrightarrow\left(-3\right)^n=\left(-27\right).81\)

\(\Leftrightarrow\left(-3\right)^n=\left(-3\right)^3.\left(-3\right)^4\)

\(\Leftrightarrow\left(-3\right)^n=\left(-3\right)^7\)

\(\Leftrightarrow n=7\)

4. Ta có:

\(\dfrac{x}{2}=\dfrac{y}{3}\Rightarrow\dfrac{x}{10}=\dfrac{y}{15}\) (1)

\(\dfrac{y}{5}=\dfrac{z}{4}\Rightarrow\dfrac{y}{15}=\dfrac{z}{12}\) (2)

Từ (1) và (2) suy ra \(\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{12}\)

Vì \(x-y+x=-49\) ta có:

\(\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{12}=\dfrac{x-y+z}{10-15+12}=\dfrac{-49}{7}=-7\)

Vậy \(\left\{{}\begin{matrix}x=\left(-7\right).10=-70\\y=\left(-7\right).15=-105\\z=\left(-7\right).12=-84\end{matrix}\right.\)