\(\left(x-\frac{1}{2}\right)^2=0\)
\(\frac{x\left(x+1\right)}{2\left(x-3\right)\left(x+1\right)}+\frac{x\left(x-3\right)}{2\left(x-3\right)\left(x+1\right)}-\frac{4x}{2\left(x-3\right)\left(x+1\right)}=0\)
\(\frac{x^2+x+x^2-3x-4x}{2\left(x-3\right)\left(x+1\right)}=0\)
\(x^2-3x=0\)
đâu phải toán lớp 1
bạn chọn nhầm à
a)\(\left(\frac{5}{7}x-\frac{1}{4}\right)\left(\frac{-3}{4}x+\frac{1}{2}\right)=0\)
b)\(\left(\frac{4}{5}+x\right).\left(x-\frac{8}{13}\right)=0\)
c)\(\left(2x-\frac{1}{2}\right).\left(x-3\right)=0\)
d)\(x+3\frac{1}{2}x+x=\frac{1}{2}\)
a) \(\left(\frac{5}{7}x-\frac{1}{4}\right)\left(\frac{-3}{4}x+\frac{1}{2}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}\frac{5}{7}x-\frac{1}{4}=0\\\frac{-3}{4}x+\frac{1}{2}=0\end{cases}}\Rightarrow\orbr{\begin{cases}\frac{5}{7}x=\frac{1}{4}\\\frac{-3}{4}x=\frac{-1}{2}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{7}{20}\\x=\frac{2}{3}\end{cases}}\)
Vậy \(x=\frac{7}{20}\) hoặc x=\(\frac{2}{3}\)
b) \(\left(\frac{4}{5}+x\right)\left(x-\frac{8}{13}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}\frac{4}{5}+x=0\\x-\frac{8}{13}=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{-4}{5}\\x=\frac{8}{13}\end{cases}}\)
Vậy x=-4/5 hoặc x=8/13
c) \(\left(2x-\frac{1}{2}\right)\left(x-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x-\frac{1}{2}=0\\x-3=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{1}{4}\\x=3\end{cases}}\)
Vậy x=1/4 hoặc x=3
\(x+\frac{7}{2}x+x=\frac{1}{2}\)
\(2x+\frac{7}{2}x=\frac{1}{2}\)
\(\left(2+\frac{7}{2}\right)x=\frac{1}{2}\)
\(\frac{11}{2}x=\frac{1}{2}\)
\(x=\frac{1}{2}:\frac{11}{2}\)
\(x=\frac{1}{11}\)
\(\frac{-3x.\left(5x+3\right)}{1+3x}>=0\)\(\frac{-2x^2+5x-3}{-x.\left(3x+7\right)}>0\)\(\frac{1}{x-2}-\frac{4}{x^2-4}< \frac{1}{3}\)\(x^2-20x+51>0\)\(\left(x-3\right).\left(2x+1\right)\left(1-5x\right)< 0\)\(\left(x-2\right)\left(x+3\right)=< 0\)
\(0=-\frac{\left(x+2\right)^2+12}{\left(x+2\right)^2}+\frac{\left(x+1\right)^2+1}{\left(x+1\right)^2}-\frac{\left(x+3\right)^2+3}{\left(x+3\right)^2}+\frac{\left(x+4\right)^2+4}{\left(x+4\right)^2}\)
giải pt
a) \(x^2+4x-3\left|x+2\right|+4=0\)
b) \(\left(x+2\right)^2-3\left|x+2\right|-4=0\)
c) \(\left(x^2-3\right)^2-6\left|x^2-3\right|+5=0\)
d) \(\frac{x^2-4x+4}{x^2-2x+1}+\frac{\left|2x-4\right|}{x-1}=3\)
e) \(\left|\frac{2x-1}{x+2}\right|-2\left|\frac{x+2}{2x-1}\right|=1\)
f) \(x^2+\frac{1}{x^2}-10=2\left|x-\frac{1}{x}\right|\)
a/ \(\Leftrightarrow\left(x+2\right)^2-3\left|x+2\right|=0\)
\(\Leftrightarrow\left|x+2\right|^2-3\left|x+2\right|=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x+2\right|=0\\\left|x+2\right|=3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-2\\x+2=3\\x+2=-3\end{matrix}\right.\)
b/
\(\Leftrightarrow\left|x+2\right|^2-3\left|x+2\right|-4=0\)
\(\Leftrightarrow\left(\left|x+2\right|+1\right)\left(\left|x+2\right|-4\right)=0\)
\(\Leftrightarrow\left|x+2\right|-4=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=4\\x+2=-4\end{matrix}\right.\)
c/
\(\Leftrightarrow\left|x^2-3\right|^2-6\left|x^2-3\right|+5=0\)
\(\Leftrightarrow\left(\left|x^2-3\right|-1\right)\left(\left|x^2-3\right|-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x^2-3\right|=1\\\left|x^2-3\right|=5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-3=1\\x^2-3=-1\\x^2-3=5\\x^2-3=-5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2=4\\x^2=2\\x^2=8\\x^2=-2\left(l\right)\end{matrix}\right.\)
d/ ĐKXĐ: ...
\(\Leftrightarrow\frac{\left|x-2\right|^2}{\left(x-1\right)^2}+\frac{2\left|x-4\right|}{x-1}=3\)
Đặt \(\frac{\left|x-2\right|}{x-1}=a\)
\(a^2+2a-3=0\Rightarrow\left[{}\begin{matrix}a=1\\a=-3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left|x-2\right|=x-1\\\left|x-2\right|=-3\left(x-1\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x-2\right|=x-1\left(x\ge1\right)\\\left|x-2\right|=3-3x\left(x\le1\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=x-1\left(vn\right)\\x-2=1-x\\x-2=3-3x\\x-2=3x-3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\frac{3}{2}\\x=\frac{4}{5}\\x=\frac{1}{2}\end{matrix}\right.\)
e/ ĐKXĐ: ...
Đặt \(\left|\frac{2x-1}{x+2}\right|=a>0\)
\(a-\frac{2}{a}=1\Leftrightarrow a^2-a-2=0\)
\(\Rightarrow\left[{}\begin{matrix}a=-1\left(l\right)\\a=2\end{matrix}\right.\) \(\Rightarrow\left|\frac{2x-1}{x+2}\right|=2\)
\(\Rightarrow\left[{}\begin{matrix}2x-1=2\left(x+2\right)\\2x-1=-2\left(x+2\right)\end{matrix}\right.\)
f/ ĐKXĐ: ...
Đặt \(\left|x-\frac{1}{x}\right|=a\ge0\Rightarrow a^2=x^2+\frac{1}{x^2}-2\Rightarrow x^2+\frac{1}{x^2}=a^2+2\)
Phương trình trở thành:
\(a^2+2-10=2a\)
\(\Leftrightarrow a^2-2a-8=0\Rightarrow\left[{}\begin{matrix}a=4\\a=-2\left(l\right)\end{matrix}\right.\)
\(\Rightarrow\left|x-\frac{1}{x}\right|=4\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\frac{1}{x}=4\\x-\frac{1}{x}=-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-4x-1=0\\x^2+4x-1=0\end{matrix}\right.\)
bt em gửi cô Thương
1)\(ĐKXĐ\hept{\begin{cases}x\ne1\\x\ne3\end{cases}}\)
\(\frac{x+5}{x-1}=\frac{x+1}{x-3}-\frac{8}{x^2-4x+3}\)
\(\Leftrightarrow\frac{x+5}{x-1}-\frac{x+1}{x-3}+\frac{8}{x^2-4x+3}=0\)
\(\Leftrightarrow\frac{x+5}{x-1}-\frac{x+1}{x-3}+\frac{8}{x^2-x-3x+3}=0\)
\(\Leftrightarrow\frac{\left(x+5\right)\left(x-3\right)}{\left(x-1\right)\left(x-3\right)}-\frac{\left(x+1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}+\frac{8}{x\left(x-1\right)-3\left(x-1\right)}=0\)
\(\Leftrightarrow\frac{x^2+2x-15}{\left(x-1\right)\left(x-3\right)}-\frac{x^2-1}{\left(x-3\right)\left(x-1\right)}+\frac{8}{\left(x-1\right)\left(x-3\right)}=0\)
\(\Leftrightarrow\frac{2x-6}{\left(x-1\right)\left(x-3\right)}=0\)
\(\Leftrightarrow2x-6=0\)
\(\Leftrightarrow x=3\)( tm)
Vậy nghiemj của pt x=3
2)\(x^3-x^2-9x+9=0\)
\(\Leftrightarrow x^2\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-9\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\x-3=0\end{cases}}\)hoặc x+3=0
\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=3\end{cases}}\)hoặc x=-3
Vậy tập hợp nghiệm \(S=\left\{1;3;-3\right\}\)
Bài 1 dài dòng quá em :( Rút gọn bớt cũng được thì phải
Chị ơi bài 1 em sai cái gì ko ạ ? đk x khác 3 mà đúng ko
Bài 1 em không làm sai gì nhưng kết quả sai. Vì đk # 3 nên kết x = 3 không thỏa mãn em ơi :v
\(1.\frac{1}{x^2-2x+2}+\frac{2}{x^2-2x+3}=\frac{6}{x^2-2x+4}
\)
2.\(\frac{2x^4}{\left(x+1\right)^2}-\frac{5x^2}{x+1}+2=0\)
3.\(\left(x+\frac{1}{x}\right)^2-6\left(x+\frac{1}{x}\right)+8=0\)
4.\(\left(x^2+\frac{1}{x^2}\right)-4\left(x+\frac{1}{x}\right)+6=0\)
5.\(\frac{2x}{3x^2-x+2}-\frac{7x}{3x^2+5x+2}=1\)
chứng minh:
\(\left(\frac{1}{2}-x\right).\left(\frac{1}{3}-x\right)>0\)
\(\left(x+\frac{2}{3}\right).\left(2-x\right)=0\)
\(^{x^2}-\frac{2}{5}.x< 0\)
1. \(\frac{x^3-10x^2+25x}{x^2-5x}\)\(=0\) ( đkxđ: \(x\ne0;5\))
<=> \(\frac{x\left(x-5\right)^2}{x\left(x-5\right)}=0\)<=> \(x-5=0\)<=> vô no
2. \(A=\)\(\frac{2x^2-2}{x^3-x^2-4x+4}\)\(=\frac{2\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x-2\right)\left(x+2\right)}\) ( a, đkxđ: \(x\ne1;\pm2\))
b, \(A=0\)<=> \(\frac{2\left(x+1\right)}{\left(x-2\right)\left(x+2\right)}=0\)<=> \(x=-1\)( TM) . Vậy \(A=0\Leftrightarrow x=-1\)
3. \(B=\frac{3x^2-12}{\left(x-3\right)\left(x^2+4x+4\right)}\)\(=\frac{3\left(x-2\right)\left(x+2\right)}{\left(x-3\right)\left(x+2\right)^2}\) ( a, đkxđ: \(x\ne3,-2\))
\(b,B=0\Leftrightarrow\frac{3\left(x-2\right)}{\left(x-3\right)\left(x+2\right)}=0\Leftrightarrow x=2\left(tm\right)\). Vậy \(B=0\Leftrightarrow x=2\)
bài 2: giải các bpt sau:
1) (x-2)(\(9-x^2\))≤0
2) (\(x^2-x-6\))(\(x^2-3x+2\))≥0
3) \(\frac{\left(x-2\right)\left(9-x\right)}{x-1}\)≤0
4) \(\frac{x\left(x^2-3x+2\right)}{x+4}\)≥0
5) \(\frac{\left(x+2\right)}{\left(x+1\right)\left(x-2\right)}\)<0
6) \(\frac{\left(x-2\right)\left(9-x^2\right)}{x-1}\)≥0
7) \(\frac{x^2\left(x-3\right)}{3x^2+x-4}\)≥0
8) \(\frac{x^2-3x+2}{9-x}\)≥0
9) \(\frac{x^2+1}{x^2+3x-10}\)≤0
10) \(\frac{x^2-9x+14}{x^2+9x+14}\)≥0