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a) \(\left(x-3\right)\left(6-x\right)>0\)
\(\Rightarrow\)\(\hept{\begin{cases}x-3>0\\6-x>0\end{cases}\Leftrightarrow\hept{\begin{cases}x>3\\x< 6\end{cases}\Leftrightarrow}3< x< 6}\)
hoặc \(\hept{\begin{cases}x-3< 0\\6-x< 0\end{cases}\Leftrightarrow\hept{\begin{cases}x< 3\\x>6\end{cases}}}\)(vô lí)
Vậy \(3< x< 6\)
1.
1.2 +2.3 +...+97.98
=1/3.(1.2.3 +2.3.3 +3.4.3 +...+97.98.3)
=1/3.(1.2.3 - 0.1.2+ 2.3.4 -1.2.3 + 3.4.5 -2.3.4 + ... +97.98.99 -96.97.98)
=1/3 . 97.98.99
= 313698
=>1.2 +2.3 +...+97.98-x=16
=>313698-x=16
=> x=313682
4.
\(\left[\left(\frac{36}{x}-x\right):x-x\right]:x-x=-x\)
\(\left[\left(\frac{36}{x}-x\right):x-x\right]:x=-x+x\)
\(\left[\left(\frac{36}{x}-x\right):x-x\right]:x=0\)
\(\left[\left(\frac{36}{x}-x\right):x-x\right]=0\)
\(\left(\frac{36}{x}-x\right):x=x\Rightarrow\frac{36}{x}-x=x^2\)
\(\frac{36}{x}=x^2+x=x\left(x+1\right)\Rightarrow36=x^2\left(x+1\right)\)
Mà Ư(36)={1;2;3;4;6;9;12;18;36}; 9 là số chính phương duy nhất bé hơn 36=> x2 = 9 => x=3
2 câu kia thì đợi một lúc.
aahkl============================================================================
c) \(x^2+2x=0\)
\(x\left(x+2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x+2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-2\end{cases}}}\)
Vậy \(x=0\)hoặc \(x=-2\)
b) \(3-\left|1-3x\right|=2x\)
\(\left|1-3x\right|=3-2x\)
\(\Rightarrow\orbr{\begin{cases}1-3x=3-2x\\1-3x=2x-3\end{cases}\Leftrightarrow\orbr{\begin{cases}-3x+2x=3-1\\-3x-2x=-3-1\end{cases}\Leftrightarrow}\orbr{\begin{cases}-x=2\\-5x=-4\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-2\\x=\frac{4}{5}\end{cases}}}\)
KL:.....................................................................
a) \(\frac{3}{4}-\frac{1}{4}x=-3x\)
\(-3x+\frac{1}{4}x=\frac{3}{4}\)
\(-\frac{11}{4}x=\frac{3}{4}\)
\(x=\frac{3}{4}:\left(-\frac{11}{4}\right)\)
\(x=\frac{3}{4}.\left(-\frac{4}{11}\right)\)
\(x=-\frac{3}{11}\)
Vậy \(x=-\frac{3}{11}\)
Tham khảo nhé~
2) \(\left(x-5\right)\left(x^2+1\right)=0\)
\(\Rightarrow x-5=0\) vì \(x^2+1>0\)
\(\Rightarrow x=5\)
cAU 1 TƯƠNG TỰ NHÉ
Tương tự sao được
a/ \(30.\left\{x+2+6\left(x-5\right)\right\}-24x=102\)
\(\Leftrightarrow30.\left\{x+2+6x-30\right\}-24x=102\)
\(\Leftrightarrow30.\left\{7x-28\right\}-24x=102\)
\(\Leftrightarrow210x-340-24x=102\)
\(\Leftrightarrow186x-340=102\)
\(\Leftrightarrow186x=442\)
\(\Leftrightarrow x=\frac{442}{186}\)
c/ \(\left(x+1\right)+\left(x+2\right)+....+\left(x+99\right)=0\)
\(\Leftrightarrow\left(x+x+...+x\right)+\left(1+2+......+99\right)=0\)
\(\Leftrightarrow99x+49500=0\)
\(\Leftrightarrow x=-50\)
\(a,2x\left(x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x=0\\x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x\in\forall Z\\x=1\end{cases}}}\)
\(b,x\left(2x-4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\2x-4=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}}\)
\(c;\left(x+1\right)+\left(x+3\right)+...............+\left(x+99\right)=0\)
\(\Rightarrow\left(x+x+...........+x\right)+\left(1+3+............+99\right)=0\)
\(\Rightarrow50x+2500=0\)
\(\Rightarrow50x=-2500\)
\(\Rightarrow x=-50\)
2/
\(a;\left(x-3\right)\left(2y+1\right)=7\)
\(\Rightarrow\left(x-3\right);\left(2y+1\right)\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
Xét bảng
| x-3 | 1 | -1 | 7 | -7 |
| 2y+1 | 7 | -7 | 1 | -1 |
| x | 4 | 2 | 10 | -4 |
| y | 3 | -4 | 0 | -1 |
Vậy...............................
\(b;xy+3x-2y=11\)
\(\Rightarrow x\left(y+3\right)-2y-6=11-6\)
\(\Rightarrow x\left(y+3\right)-2\left(y+3\right)=5\)
\(\Rightarrow\left(x-2\right)\left(y+3\right)=5\)
\(\Rightarrow\left(x-2\right);\left(y+3\right)\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)
Xét bảng'
| x-2 | 1 | -1 | 5 | -5 |
| y+3 | 5 | -5 | 1 | -1 |
| x | 3 | 1 | 7 | -3 |
| y | 2 | -8 | -2 | -4 |
Vậy................................
\(\frac{3}{4}x-\frac{2}{3}x=\frac{10}{21}\)
<=> \(x\left(\frac{3}{4}-\frac{2}{3}\right)=\frac{10}{21}\)
<=> \(\frac{1}{12}x=\frac{10}{21}\)
<=> \(x=\frac{40}{7}\)
\(\left(x-1\right)\left(x+2\right)< 0\)
<=> \(\hept{\begin{cases}x-1< 0\\x+2>0\end{cases}}\)hoặc \(\hept{\begin{cases}x-1>0\\x+2< 0\end{cases}}\)
<=> \(\hept{\begin{cases}x< 1\\x>-2\end{cases}}\)hoặc \(\hept{\begin{cases}x>1\\x< -2\end{cases}}\)
<=> \(-2< x< 1\)hoẵ \(x\)thuộc rỗng
<=> \(-2< x< 1\)
a. 3/4.x -2/3.x = 10/21
(3/4 -2/3).x = 10/21
1/12.x = 10/21
x = 10/21 :1/12
x = 40/7