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\(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\left(-3,2\right)+\frac{2}{5}\)
\(\Rightarrow\left|x-\frac{1}{3}\right|+\frac{4}{5}=\frac{-14}{5}\)
\(\Rightarrow\left|x-\frac{1}{3}\right|=\frac{-14}{5}-\frac{4}{5}\)
\(\Rightarrow\left|x-\frac{1}{3}\right|=\frac{-18}{5}\)
Vì giá trị tuyệt đối không thể là một số âm
\(\Rightarrow x\in\varnothing\)
\(6.8^{x-1}+8^{x+1}=6.8^{19}+8^{21}\)
\(\Rightarrow\hept{\begin{cases}x-1=19\\x+1=21\end{cases}\Rightarrow\hept{\begin{cases}x=20\\x=20\end{cases}}}\)
\(5.2^x+3.2^{x+2}=5.2^5+3.2^7\)
\(\Rightarrow\hept{\begin{cases}x=5\\x+2=7\end{cases}\Rightarrow\hept{\begin{cases}x=5\\x=5\end{cases}}}\)
P/s:Kết quả thì chắc chắn đúng nhưng cách trình bày bài giải có thể sai,mong bn thông cảm =.=
\(2^{x-2}-3.2^x=-88\)
\(2^x:2^2-2^x:\frac{1}{3}=-88\)
\(2^x:\left(2^2-\frac{1}{3}\right)=-88\)
\(2^x:\frac{11}{3}=-88\)
\(2^x=-88.\frac{11}{3}\)
\(2^x=\frac{-968}{3}\)
\(2^{x-2}-\)\(3.2^x=-88\)
\(2^x:2^2-2^x.3=-88\)
\(2^x.\frac{1}{4}-\)\(2^x.3=-88\)
\(2^x.\left(\frac{1}{4}-3\right)=-88\)
\(2^x.\frac{-11}{4}=-88\)
\(2^x=-88:\frac{-11}{4}\)
\(2^x=32\)
\(2^x=2^5\)
\(\Rightarrow x=5\)
\(\left(x-\frac{1}{3}\right)+\frac{4}{5}=\left[\left(-3.2\right)+\frac{2}{5}\right]\)
\(\left(x-\frac{1}{3}\right)+\frac{4}{5}=\left(-6+\frac{2}{5}\right)\)
\(\left(x-\frac{1}{3}\right)+\frac{4}{5}=-\frac{28}{5}\)
\(x-\frac{1}{3}=-\frac{28}{5}+\frac{4}{5}\)
\(x-\frac{1}{3}=-\frac{24}{5}\)
\(x=-\frac{24}{5}+\frac{1}{3}\)
\(x=-\frac{67}{15}\)
đúng thì k tớ nha bn
Ta có :
\(\hept{\begin{cases}\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{10}=\frac{y}{15}\\\frac{y}{5}=\frac{z}{7}\Rightarrow\frac{y}{15}=\frac{z}{21}\end{cases}}\)
\(\Rightarrow\frac{x}{10}=\frac{y}{15}=\frac{z}{21}\)
Theo tính chất của dãy tỉ số bằng nhau ta có :
\(\frac{x}{10}=\frac{y}{15}=\frac{z}{21}=\frac{x+y+z}{10+15+21}=\frac{92}{46}=2\)
\(\Rightarrow x=2\times10=20\)
\(\Rightarrow y=2\times15=30\)
\(\Rightarrow z=2\times21=42\)
k cho mk nha
\(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{10}=\frac{y}{15}\); \(\frac{y}{5}=\frac{z}{7}\Rightarrow\frac{y}{15}=\frac{z}{21}\)
\(\Rightarrow\frac{x}{10}=\frac{y}{15}=\frac{z}{21}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có :
\(\frac{x}{10}=\frac{y}{15}=\frac{z}{21}=\frac{x+y+z}{10+15+21}=\frac{92}{46}=2\)
\(\Rightarrow x=20;y=30;z=42\)
Ta có : \(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{10}=\frac{y}{15}\)(1)
\(\frac{y}{5}=\frac{z}{7}\Rightarrow\frac{y}{15}=\frac{z}{21}\) (2)
Từ (1) và (2) => \(\frac{x}{10}=\frac{y}{15}=\frac{z}{21}\)
Ta có : \(\frac{x}{10}=\frac{y}{15}=\frac{z}{21}=\frac{x+y+z}{10+15+21}=\frac{92}{46}=2\)
Nên : \(\frac{x}{10}=2\Rightarrow x=20\)
\(\frac{y}{15}=2\Rightarrow y=30\)
\(\frac{z}{21}=2\Rightarrow z=42\)
Vậy x = 20 , y = 30 , z = 42 .
\(2^{x-2}-3.2^x=-88\)
\(\Leftrightarrow2^x.\frac{1}{4}-3.2^x=-88\)
\(\Leftrightarrow2^x\left(\frac{1}{4}-3\right)=-88\)
\(\Leftrightarrow2^x.\frac{-11}{4}=-88\)
\(\Leftrightarrow2^x=-88.\frac{-4}{11}\)
\(\Leftrightarrow2^x=-8.\left(-4\right)\)
\(\Leftrightarrow2^x=32=2^5\)
\(\Leftrightarrow x=5\)
Vậy x = 5
a. \(\frac{x}{2}=\frac{y}{3}=k\Rightarrow x=2k;y=3k\)
\(xy=54\Rightarrow2k3k=54\Rightarrow6k^2=54\Rightarrow k^2=9\Rightarrow k\in\left\{3;-3\right\}\)
\(k=3\Rightarrow x=6;y=9\)
\(k=-3\Rightarrow x=-6;y=-9\)
b.\(\frac{x}{5}=\frac{y}{3}=k\Rightarrow x=5k;y=3k\)
\(\Rightarrow\left(5k\right)^2-\left(3k\right)^2=4\Rightarrow25k^2-9k^2=4\)
\(\Rightarrow16k^2=4\Rightarrow k^2=\frac{1}{4}\Rightarrow k\in\left\{\frac{1}{2};-\frac{1}{2}\right\}\)
\(k=\frac{1}{2}\Rightarrow x=\frac{5}{2};y=\frac{3}{2}\)
\(k=-\frac{1}{2}\Rightarrow x=\frac{-5}{2};y=\frac{-3}{2}\)
c.\(\frac{x}{2}=\frac{y}{3}\Rightarrow\frac{x}{2}.\frac{1}{5}=\frac{y}{3}.\frac{1}{5}\Rightarrow\frac{x}{10}=\frac{y}{15}\)
\(\frac{y}{5}=\frac{z}{7}\Rightarrow\frac{y}{5}.\frac{1}{3}=\frac{z}{7}.\frac{1}{3}\Rightarrow\frac{y}{15}=\frac{z}{21}\)
\(\Rightarrow\frac{x}{10}=\frac{y}{15}=\frac{z}{21}=\frac{x+y+z}{10+15+21}=\frac{92}{46}=2\)
\(\Rightarrow x=20,y=30,z=42\)
d.\(\frac{x^2}{9}=\frac{y^2}{16}\Rightarrow\frac{x^2}{9}=\frac{y^2}{16}=\frac{x^2+y^2}{9+16}=\frac{100}{25}=4\)
\(\Rightarrow x^2=36\Rightarrow x\in\left\{6;-6\right\};y^2=64\Rightarrow y\in\left\{8;-8\right\}\)
\(2^{x-3}-3.2^x=-92\)
\(\Rightarrow2^x\left(2^{-3}-3\right)=-92\)
\(\Rightarrow2^x.\dfrac{-23}{8}=-92\Rightarrow2^x=32\)
\(\Rightarrow2^x=2^5\Rightarrow x=5\)