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a)
\(\left\{{}\begin{matrix}\left(4x-1\right)^4\ge0\\\left|2x-3y\right|\ge0\end{matrix}\right.\) \(\Rightarrow A\ge25,6\) tự tìm cận
không có Max
b) giống vậy
c) \(\left\{{}\begin{matrix}\left(x-3\right)^2\ge0\Rightarrow-\left(x-3\right)^2\le0\\\left|4x-3y\right|\ge0\Rightarrow-\left|4x-3y\right|\le0\end{matrix}\right.\)
\(C\le40,5\) tự tìm cận
không có GTNN
a.\(\left(3x-2\right)^2=16\)
Ta có: \(\left(3x-2\right)^2=16\)
\(\Rightarrow\left(3x-2\right)^2=\left(4\right)^2\)
\(\Rightarrow3x-2=4\)
\(\Rightarrow3x=6\)
\(\Rightarrow x=2\)
b. \(\left(\dfrac{4}{5}x-\dfrac{3}{4}\right)^3=\dfrac{-8}{125}\)
\(\Rightarrow\left(\dfrac{4}{5}x-\dfrac{3}{4}\right)^3=\left(\dfrac{-2}{5}\right)^3\)
\(\Rightarrow\dfrac{4}{5}x-\dfrac{3}{4}=\dfrac{-2}{5}^{ }\)
\(\Rightarrow\dfrac{4}{5}x-=\dfrac{7}{20}\)
\(\Rightarrow x=\dfrac{7}{16}\)
a) \(\left|2,5-x\right|-1,3=0\)
th1: \(2,5-x\ge0\Leftrightarrow x\le2,5\)
\(\Rightarrow\left|2,5-x\right|-1,3=0\Leftrightarrow2,5-x-1,3=0\Leftrightarrow x=1,2\left(tmđk\right)\)
th2: \(2,5-x< 0\Leftrightarrow x>2,5\)
\(\Rightarrow\left|2,5-x\right|-1,3=0\Leftrightarrow x-2,5-1,3=0\Leftrightarrow x=3,8\left(tmđk\right)\)
vậy \(x=1,2;x=3,8\)
b) \(1,6.\left|x-0,2\right|=0\Leftrightarrow\left|x-0,2\right|=0\Leftrightarrow x-0,2=0\Leftrightarrow x=0,2\) vậy \(x=0,2\)
c) \(\left|\dfrac{1}{3}-x\right|-\left|\dfrac{-3}{7}\right|=0\)
th1: \(\dfrac{1}{3}-x\ge0\Leftrightarrow x\le\dfrac{1}{3}\)
\(\Rightarrow\left|\dfrac{1}{3}-x\right|-\left|\dfrac{-3}{7}\right|=0\Leftrightarrow\dfrac{1}{3}-x-\dfrac{3}{7}=0\Leftrightarrow x=\dfrac{-2}{21}\left(tmđk\right)\)
th2: \(\dfrac{1}{3}-x< 0\Leftrightarrow x>\dfrac{1}{3}\)
\(\Rightarrow\left|\dfrac{1}{3}-x\right|-\left|\dfrac{-3}{7}\right|=0\Leftrightarrow x-\dfrac{1}{3}-\dfrac{3}{7}=0\Leftrightarrow x=\dfrac{16}{21}\left(tmđk\right)\)
vậy \(x=\dfrac{-2}{21};x=\dfrac{16}{21}\)
d) \(\left|x+\dfrac{4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\)
th1: \(x+\dfrac{4}{15}\ge0\Leftrightarrow x\ge\dfrac{-4}{15}\)
\(\Rightarrow\left|x+\dfrac{4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\Leftrightarrow x+\dfrac{4}{15}-3,75=-2,15\)
\(\Leftrightarrow x=\dfrac{4}{3}\left(tmđk\right)\)
th2: \(x+\dfrac{4}{15}< 0\Leftrightarrow x< \dfrac{-4}{15}\)
\(\Rightarrow\left|x+\dfrac{4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\Leftrightarrow-x-\dfrac{4}{15}-3,75=-2,15\)
\(\Leftrightarrow x=\dfrac{-28}{15}\left(tmđk\right)\)
vậy \(x=\dfrac{4}{3};x=\dfrac{-28}{15}\)
e) ta có : \(\left|x-1,5\right|\ge0\forall x\) và \(\left|2,5-x\right|\ge0\forall x\)
\(\Rightarrow\left|x-1,5\right|+\left|2,5-x\right|=0\Leftrightarrow\left\{{}\begin{matrix}x-1,5=0\\2,5-x=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1,5\\x=2,5\end{matrix}\right.\) 2 giá trị này khác nhau \(\Rightarrow\) phương trình vô nghiệm
a) Vì \(\left|2,5-x\right|=1,3\Rightarrow\left\{{}\begin{matrix}2,5-x=1,3\\2,5-x=-1,3\end{matrix}\right.\left\{{}\begin{matrix}x=1,2\\x=3,8\end{matrix}\right.\)
b) \(1,6-\left|x-0,2\right|=0\)
\(\Rightarrow\left|x-0,2\right|=1,6\)
Vì \(\left|x-0,2\right|=1,6\Rightarrow\left\{{}\begin{matrix}x-0,2=1,6\\x-0,2=-1,6\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=1,8\\x=-1,4\end{matrix}\right.\)
c) Vì \(\left|x-1,5\right|\ge0;\left|2,5-x\right|\ge0\)
Mà \(\left|x-1,5\right|+\left|2,5-x\right|=0\left\{{}\begin{matrix}x-1,5=0\\2,5-x=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=1,5\\x=2,5\end{matrix}\right.\)
Vô lý vì \(x\) không thể nhận đồng thời 2 giá trị \(\Rightarrow x\) không có giá trị thỏa mãn đề bài
a. Vì |2,5 – x| = 1,3 nên 2,5 – x =1,3
=> x = 2,5 – 1,3 => x = 1,2
Hoặc 2,5 – x = -1,3 => x = 2,5 – ( -1,3)
=> x = 2,5 + 1,3 => x = 3,8
Vậy x = 1,2 hoặc x = 3,8
b. 1,6 - | x – 0,2| = 0 => |x – 0,2 | =1,6 nên x – 0,2 – 1,6
=> x = 1,6 + 0,2 => x = 1,8
Hoặc x – 0,2 = -1,6 => x= -1,6 + 0,2 => x = -1,4
Vậy x = 1,8 hoặc x = -1,4
c. |x – 1,5 | + | 2,5 – x | = 0 nên |x – 1,5| ≥ 0 ; |2,5 – x| ≥ 0
Suy ra: x – 1,5 = 0; 2,5 – x = 0 => x= 1,5 và x = 2,5
Điều này không đồng thời xảy ra. Vậy không có giá trị nào của x thoả mãn bài toán.
a) \(\left|x\left(x-7\right)\right|=x\)
\(\Rightarrow\orbr{\begin{cases}x\left(x-7\right)=x\\x\left(x-7\right)=-x\end{cases}\Leftrightarrow\orbr{\begin{cases}x-7=1\\x-7=-1\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=8\\x=6\end{cases}}}\)
b) \(\left|x-1,1\right|+\left|x+1,2\right|+\left|x+1,3\right|+\left|x+1,4\right|=5x\)
\(\Rightarrow x-1,1+x+1,2+x+1,3+x+1,4=5x\)
\(\Leftrightarrow4x+2,8=5x\)
\(\Leftrightarrow x=2,8\)
\(a.\)\(\left|x.\left(x-7\right)\right|=x\)( Đk: \(x\ge0\))
\(\Leftrightarrow\orbr{\begin{cases}x.\left(x-7\right)=x\\x.\left(x-7\right)=-x\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-7=x:x\\x-7=-x:x\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-7=1\\x-7=-1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=1+7\\x=-1+7\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=8\\x=6\end{cases}}\)
\(b.\)\(\left|x-1,1\right|+\left|x+1,2\right|+\left|x+1,3\right|+\left|x+1,4\right|=5x\)( Đk: \(5x\ge0\Leftrightarrow x\ge0\))
\(\Rightarrow x-1,1+x+1,2+x+1,3+x+1,4=5x\)
\(\Leftrightarrow\left(x+x+x+x\right)+\left(-1,1+1,2+1,3+1,4\right)=5x\)
\(\Leftrightarrow4x+2,8=5x\)
\(\Leftrightarrow2,8=5x-4x\)
\(\Leftrightarrow x=2,8\)
\(c.\)\(7^{x+2}+2.7^{x-1}=345\)
\(\Leftrightarrow7^{x-1}.7^{x+3}+2.7^{x-1}=345\)
\(\Leftrightarrow7^{x-1}.\left(7^{x+3}+2\right)=345\)
\(......................\)
Đến đây mk ko bt làm nữa, tự lm nhé !
Câu a,b,c,d link đây Câu hỏi của (っ◔◡◔)っ ♥ GDragon Huyền Tồ ♥
e) \(\left|3x-1\right|=\left(9,103-4,659\right):\dfrac{3}{2}\)
\(\left|3x-1\right|=4,444:\dfrac{3}{2}\)
\(\left|3x-1\right|=\dfrac{4444}{1000}:\dfrac{3}{2}\)
\(\left|3x-1\right|=\dfrac{4444.2}{1000.3}=\dfrac{4444}{1500}\)
____* \(3x-1=\dfrac{4444}{1500}\)
\(3x=\dfrac{4444}{1500}+1\)
\(3x=\dfrac{5944}{1500}\)
\(x=\dfrac{5944}{4500}=\dfrac{1486}{1125}\)
____* \(3x-1=-\dfrac{4444}{1500}\)
\(3x=-\dfrac{4444}{1500}+1\)
\(x=-\dfrac{2944}{4500}=-\dfrac{736}{1125}\)
P/s: ( Nếu có sai chỗ nào thì sửa giùm nha đang cấn trận đánh bang bang hay rồi nên phải nhanh )
a/ \(\left|2x-1,6\right|-2,3=1,4\)
\(\Leftrightarrow\left|2x-1,6\right|=3,7\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1,6=3,7\\2x-1,6=-3,7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=5,3\\2x=-2,1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2,65\\x=-1,05\end{matrix}\right.\)
Vậy ....
b/ \(5,4-\left|3x-1,2\right|=5,5\)
\(\Leftrightarrow\left|3x-1,2\right|=-0,1\)
Mà \(\left|3x-1,2\right|\ge0\)
\(\Leftrightarrow x\in\varnothing\)
c/ \(\left|x+1,3\right|+\left|x+2,4\right|=4x\)
Mà \(\left\{{}\begin{matrix}\left|x+1,3\right|\ge0\\\left|x+2,4\right|\ge0\end{matrix}\right.\) \(\Leftrightarrow4x\ge0\)
\(\Leftrightarrow x+1,3+x+2,4=4x\)
\(\Leftrightarrow2x+3,7=4x\)
\(\Leftrightarrow3,7=4x-2x\)
\(\Leftrightarrow2x=3,7\)
\(\Leftrightarrow x=1,85\)
Vậy ....
d/ \(\left|x-1,2\right|+\left|2,5-x\right|=0\)
Mà \(\left\{{}\begin{matrix}\left|x-1,2\right|\ge0\\\left|2,5-x\right|\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x-1,2\right|=0\\\left|2,5-x\right|=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1,2=0\\2,5-x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1,2\\x=2,5\end{matrix}\right.\) (loại)
Vậy ..
a, \(\left|2x-1,6\right|-2,3=1,4\)
\(\Rightarrow\left|2x-1,6\right|=3,7\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1,6=3,7\\2x-1,6=-3,7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2,65\\x=-1,05\end{matrix}\right.\)
b,\(5,4-\left|3x-1,2\right|=5,5\)
\(\Rightarrow\left|3x-1,2\right|=-0,1\) (vô lí)
Vì \(\left|x\right|\ge0\) mà \(\left|3x-1,2\right|< 0\)
Vậy, không có giá trị của x thỏa mãn.
c, \(\left|x+1,3\right|+\left|x+2,4\right|=4x\)
\(\Rightarrow\left\{{}\begin{matrix}\left|x+1,3\right|\ge0\\\left|x+2,4\right|\ge0\end{matrix}\right.\Leftrightarrow4x\ge0\)
\(\Leftrightarrow x+1,3+x+2,4=4x\)
\(\Leftrightarrow x+x+1,3+2,4=4x\)
\(\Leftrightarrow2x+3,7=4x\)
\(\Leftrightarrow2x-4x=-3,7\)
\(\Leftrightarrow-2x=-3,7\)
\(\Leftrightarrow x=\dfrac{3,7}{2}\)
d, \(\left|x-1,2\right|+\left|2,5-x\right|=0\)
\(\Rightarrow\left\{{}\begin{matrix}\left|x-1,2\right|\ge0\\\left|2,5-x\right|\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x-1,2\right|=0\\\left|2,5-x\right|=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-1,2=0\\2,5-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1,2\\x=2,5\end{matrix}\right.\)