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\(1,x-\dfrac{2}{7}=\dfrac{4}{3};x=\dfrac{4}{3}+\dfrac{2}{7}=\dfrac{34}{21}\)
\(2,x+\dfrac{3}{4}=\dfrac{6}{8};x=\dfrac{6}{8}-\dfrac{3}{4}=0\)
\(3,\left|x\right|-\dfrac{3}{4}=\dfrac{2}{3}+\dfrac{1}{4}=\dfrac{11}{12};\left|x\right|=\dfrac{11}{12}+\dfrac{3}{4};\left|x\right|=\dfrac{5}{3}\Rightarrow x=\left[{}\begin{matrix}\dfrac{-5}{3}\\\dfrac{5}{3}\end{matrix}\right.\)
\(4,\left(x+1\right).3=4.5=20;x+1=\dfrac{20}{3}\Leftrightarrow x=\dfrac{17}{3}\)
đề là tìm n nguyên để biểu thức nguyên hả bạn ?
d, \(\frac{3n+1}{n-2}=\frac{3\left(n-2\right)+7}{n-2}=3+\frac{7}{n-2}\)ĐK : \(n\ne2\)
\(\Rightarrow n-2\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
n - 2 | 1 | -1 | 7 | -7 |
n | 3 | 1 | 9 | -5 |
tương tự
\(\Rightarrow x\left(2y+1\right)-3\left(2y+1\right)=7\)
\(\Leftrightarrow\left(x-3\right)\left(2y+1\right)=7=1.7=7.1=-1.-7=-7.-1\)
x-3 | -7 | -1 | 1 | 7 |
2y+1 | -1 | -7 | 7 | 1 |
x | -4 | 2 | 4 | 10 |
y | -1 | -4 | 3 | 0 |
vậy....
\(\dfrac{25^3.2^{10}}{16^2.625^2}=\dfrac{25^3.2^{10}}{2^8.25^2}=\dfrac{25.2^2}{1}=25.4=100.\)
10^100 + 23
= 1000...000 + 23
= 1000...023
=> A có tổng là 2 + 3 + 1 = 6 => ko chia hết
...sai đề...
|x+3|+|y-1|=0
\(\Rightarrow\hept{\begin{cases}\left|x+3\right|\ge0\\\left|y-1\right|\ge0\end{cases}\Rightarrow}\hept{\begin{cases}x+3=0\\y-1=0\end{cases}\Rightarrow}\hept{\begin{cases}x=-3\\y=1\end{cases}}\)
Vậy x=-3 ; y=1
\(x\left(x+y+z\right)=10\) (1)
\(y\left(y+z+x\right)=25\) (2)
\(z\left(z+x+y\right)=-10\) (3)
Lấy (1) + (2) + (3) theo vế ta có:
\(x\left(x+y+z\right)+y\left(y+z+x\right)+z\left(z+x+y\right)=10+25-10\)
\(\Leftrightarrow\)\(\left(x+y+z\right)^2=25\)
\(\Leftrightarrow\)\(x+y+z=\pm\sqrt{25}=\pm5\)
Nếu \(x+y+z=5\) thì: \(\hept{\begin{cases}x=2\\y=5\\z=-2\end{cases}}\)
Nếu \(x+y+z=-5\)thì \(\hept{\begin{cases}x=-2\\y=-5\\z=2\end{cases}}\)
Vậy...
10.
\(A=\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)...\left(\dfrac{3^6}{9}-81\right)....\left(\dfrac{3^{2000}}{2003}-81\right)\)
\(=\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)...\left(\dfrac{729}{9}-81\right)...\left(\dfrac{3^{2000}}{2003}-81\right)\)
mà \(\dfrac{729}{9}-81=0\Rightarrow A=0\)
\(\left(\dfrac{3}{4}-81\right).\left(\dfrac{3^2}{5}-81\right).\left(\dfrac{3^3}{6}-81\right).....\left(\dfrac{3^{2000}}{2003}-81\right)\)
\(=\left(\dfrac{3}{4}-81\right).\left(\dfrac{3^2}{5}-81\right).\left(\dfrac{3^3}{6}-81\right).....\left(\dfrac{3^6}{9}-81\right).....\left(\dfrac{3^{2000}}{2003}-81\right)\)
\(=\left(\dfrac{3}{4}-81\right).\left(\dfrac{3^2}{5}-81\right).\left(\dfrac{3^3}{6}-81\right).....0.....\left(\dfrac{3^{2000}}{2003}-81\right)\)
\(=0\)