\(a,5,5-\left|x-0,4\right|=-1\frac{1}{5}\)

\(\Rightarrow5,5-\left|x-0,4\right|=-\frac{6}{5}\)

\(\Rightarrow-\left|x-0,4\right|=-\frac{6}{5}-5,5=-6,7\)

\(\Rightarrow\left|x-0,4\right|=6,7\)

\(\Rightarrow x-0,4=\pm6,7\)

\(\Rightarrow\orbr{\begin{cases}x-0,4=6,7\\x-0,4=-6,7\end{cases}\Rightarrow\orbr{\begin{cases}x=7,1\\x=-6,3\end{cases}}}\)

\(a,5,5-\left|x-0,4\right|=-1\frac{1}{5}\)

=> \(\left|x-0,4\right|=5,5-\left[-\frac{6}{5}\right]=5,5+1,2=6,7\)

=> \(\left|x-0,4\right|=\pm6,7\)

Xét hai trường hợp :

TH1 : x - 0,4 = 6,7

=> x  = 6,7 + 0,4 = 7,1

TH2 : x - 0,4 = -6,7

=> x = -6,7 + 0,4 =-6,3

\(b,\left[1-\frac{3}{4}\left|x\right|\right]^2=\frac{16}{25}\)

=> \(\left[1-\frac{3}{4}\left|x\right|\right]=\pm\sqrt{\frac{16}{25}}\)

=> \(\left[1-\frac{3}{4}\left|x\right|\right]=\pm\frac{4}{5}\)

=> \(\orbr{\begin{cases}1-\frac{3}{4}\left|x\right|=\frac{4}{5}\\1-\frac{3}{4}\left|x\right|=-\frac{4}{5}\end{cases}}\)=> \(\orbr{\begin{cases}x=\pm\frac{4}{15}\\x=\pm\frac{12}{5}\end{cases}}\)

\(c,\left[0,1\left|x\right|-\frac{1}{2}\right]\left[0,5-\left|x\right|\right]=0\)

=> \(\orbr{\begin{cases}0,1\left|x\right|-\frac{1}{2}=0\\0,5-\left|x\right|=0\end{cases}}\)

=> \(\orbr{\begin{cases}\frac{1}{10}\left|x\right|=\frac{1}{2}\\\left|x\right|=0,5\end{cases}}\)

=> \(\orbr{\begin{cases}\left|x\right|=5\\\left|x\right|=0,5\end{cases}}\)=> \(\orbr{\begin{cases}x\in\left\{5;-5\right\}\\x\in\left\{0,5;-0,5\right\}\end{cases}}\)

d, Xét hai trường hợp rồi ra kết quả thôi

ta có: \(\frac{1}{3^2}< \frac{1}{2.3};\frac{1}{4^2}< \frac{1}{3.4};...;\frac{1}{100^2}< \frac{1}{99.100}\)

=> \(\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}=\frac{1}{2}-\frac{1}{100}< \frac{1}{2}\)

=> đpcm

đặt \(A=\frac{10^{18}+1}{10^{19}+1};B=\frac{10^{19}+1}{10^{20}+1}\)

ta có: \(10A=\frac{10^{19}+1+9}{10^{19}+1}=1+\frac{9}{10^{19}+1}\)

\(10B=\frac{10^{20}+1+9}{10^{20}+1}=1+\frac{9}{10^{20}+1}\)

mà \(\frac{9}{10^{19}+1}>\frac{9}{10^{20}+1}\)

=> 10A >10B

=> A > B

A=(9-3/5+2/3)-(7+7/5-3/2)-(9/5+5/2)

A=9 -3/5 +2/3-7-7/5+3/2-9/5-5/2

A=(9-7)-(3/5+7/5 +9/5)+(3/2-5/2)+2/3

=2-19/5-1+2/3= -32/15

What ? Ko có n thỏa mãn nha!

(1/2)^n = 1/8 => n = 3

= \(\frac{1.3.5...19}{22.24....40}\)( triệt tiêu 21 . 23 . 25 ... 39 ) = \(\frac{1.3.5.7...19}{2^{10}.11.12...20}\)=\(\frac{1.3.7.9...19}{2^{15}.6.7.8.9.10}\)=\(\frac{1.3.5}{2^{18}.3.4.5}=\frac{1}{2^{20}}\)

2^n.2=8

2^n+1=2^3

n+1=3

n=2

TL :

=> 2ⁿ . 2 = 8

=> 2^{n+ 1} = 2³

=> n + 1 = 3

=> n = 2

Hok tốt nhé :D

(-2)^n.4=-32

(-2)^n.(-2)^2=(-2)^5

(-2)^n=-2^3

n=3

\(\frac{-32}{\left(-2\right)^n}=4\)

\(\Rightarrow\left(-2\right)^n=\frac{-32\cdot1}{4}\)

\(\Rightarrow\left(-2\right)^n=-8\)

\(\Rightarrow\left(-2\right)^3=-8\)

\(\Rightarrow n=3\)

ta có (0.8)^5=(0.4x2)^5=0.4^5x2^5

         0.4^6=0.4^5x0.4

Suy ra:0.8^5/0.4^6=0.4^5x2^5/0.4^5x0.4=2^5/0.4=32/0.4=80

thank