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Taco: (x - 2)^2>0 hoac = 0
suy ra : (x - 2 )^2 + 19 > hoac = 0
dau bang xay ra khi:
x - 2 = 0
x = 2 thi y =19
Bài 2 : ta có:-I2x -5I < 0
dấu bằng xảy ra khi :
23 - I2x - 5I<hoặc = 0
suy ra : 2x -5 = 0
x = 5/2
\(C=\frac{2x^3-5x+3}{2x-1}=\frac{\left(2x^3-2x\right)-\left(3x-3\right)}{2x-1}=\frac{2x\left(x^2-1\right)-3\left(x-1\right)}{2x-1}\)
\(=\frac{2x\left(x-1\right)\left(x+1\right)-3\left(x-1\right)}{2x-1}=\frac{\left(x-1\right)\left(2x^2+2x-3\right)}{2x-1}\)
Có: \(x=\left|\frac{3}{2}\right|=\frac{3}{2}\) thì
\(C=\frac{\left(\frac{3}{2}-1\right)\left(2\cdot\frac{3^2}{2^2}+2\cdot\frac{3}{2}-3\right)}{2\cdot\frac{3}{2}-1}=\frac{\frac{1}{2}\cdot\frac{9}{2}}{2}=\frac{9}{4}\cdot\frac{1}{2}=\frac{9}{8}\)
\(\frac{2}{5}-\left|\frac{1}{2}-x\right|=6\)
\(\left|\frac{1}{2}-x\right|=\frac{2}{5}-6\)
\(\left|\frac{1}{2}-x\right|=\frac{-28}{5}\)
vì | 1/2 - x | \(\ge\)0 \(\forall\)x nên x không tồn tại
\(\frac{2}{5}-\left|\frac{1}{2}-x\right|=6\)
\(\left|\frac{1}{2}-x\right|=\frac{2}{5}-6\)
\(\left|\frac{1}{2}-x\right|=\frac{-28}{5}\)
Vì \(\left|\frac{1}{2}-x\right|=\frac{-28}{5}\)
=> x ko tồn tại
\(\left|x+\frac{3}{5}\right|=\left|x-\frac{7}{3}\right|\Rightarrow x+\frac{3}{5}=\left|x-\frac{7}{3}\right|\)
th1 : | x-7/3| =x-7/3 khi x>=7/3
x+3/5=x-7/3
0x=-44/15 ( vô lý)
=> pt vô nghiệm
th2 |x-7/3|=7/3-x khi x<=7/3
x+3/5=7/3-x
2x=26/15
x=13/15 ( tmđk)
x=13/15 là nghiệm của pt
Tham khảo tại Linh : https://olm.vn/hoi-dap/detail/242726498820.html?pos=566667058724
\(\left|x+\frac{1}{2}\right|+\left|x+\frac{1}{3}\right|+\left|x+\frac{1}{4}\right|=4x.\)
Điều kiện \(4x\ge0\)nên
\(x+\frac{1}{2}+x+\frac{1}{3}+x+\frac{1}{4}=4x\)
\(\Leftrightarrow3x+\frac{13}{12}=4x\)
\(\Leftrightarrow4x-3x=\frac{13}{12}\)
\(\Leftrightarrow x=\frac{13}{12}\)
a) \(\left|2-x\right|+x=-3\\ \Rightarrow\left|2-x\right|=-3-x\left(ĐK:-3-x\ge0\right)\\ \Rightarrow\left[{}\begin{matrix}2-x=-3-x\\2-x=3+x\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-x=-3-2\\-x-x=3-2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}0=-5\left(\text{vô lí}\right)\\-2x=1\end{matrix}\right.\Rightarrow x=\frac{-1}{2}\left(ktm\text{ }-3-x\ge0\right)\)
Vậy \(x\in\varnothing\)
b) \(\left|x-1\right|+1=2x-3\\ \Rightarrow\left|x-1\right|=2x-4\left(ĐK:2x-4\ge0\right)\\ \Rightarrow\left[{}\begin{matrix}x-1=2x-4\\x-1=-2x+4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x-x=4-1\\x+2x=1+4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\left(t/m\right)\\3x=5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\left(t/m\right)\\x=\frac{5}{3}\left(ktm\right)\end{matrix}\right.\)
Vậy x = 3
c) \(\left|\frac{4}{3}x-\frac{4}{3}+\frac{1}{2}\right|=\left|2x-2+\frac{1}{3}\right|\\ \Rightarrow\left[{}\begin{matrix}\frac{4}{3}x-\frac{4}{3}+\frac{1}{2}=2x-2+\frac{1}{3}\\\frac{4}{3}x-\frac{4}{3}+\frac{1}{2}=-2x+2-\frac{1}{3}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x-\frac{4}{3}x=2-\frac{1}{3}-\frac{4}{3}+\frac{1}{2}\\\frac{4}{3}x+2x=\frac{4}{3}-\frac{1}{2}+2-\frac{1}{3}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\frac{2}{3}x=\frac{5}{6}\\\frac{10}{3}x=\frac{5}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{5}{4}\\x=\frac{3}{4}\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{5}{4};\frac{3}{4}\right\}\)
\(\frac{2I7x+5I+11}{I7x+5I+14}\)=\(\frac{2\cdot11}{14}\)=\(\frac{22}{14}\)=\(\frac{11}{7}\)