a) Ta có: \(\left|2x-1\right|=\left|2x+3\right|\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=2x+3\left(loại\right)\\2x-1=-2x-3\end{matrix}\right.\Leftrightarrow2x+2x=-3+1\)
\(\Leftrightarrow4x=-2\)
hay \(x=-\dfrac{1}{2}\)
tìm x trong các đẳng thức:
a) \(\left|2x-3\right|=5\) b)\(\left|2x-1\right|=\left|2x=3\right|\)
c) \(\left|x-1\right|+3x=11\) d)\(\left|5x-3\right|-x=7\)
chứng minh rằng giá trị của các biểu thức sau ko phụ thuộc vào biến
a, \(x^2-2x-\left(3x^2-5x+4\right)+\left(2x^2-3x+7\right)\)
b,\(\left(2x^3-4x^2+x-1\right)-\left(5-x^2+2x^3\right)+3x^2-x\)
c, \(\left(1-x-\dfrac{3}{5}x^2\right)-\left(x^4-2x-6\right)+0,6x^2+x^4-x\)
thực hiện phép tính
a.\(5x^2-3x\left(x+2\right)\)
b.\(3x\left(x-5\right)-5x\left(x+7\right)\)
c.\(3x^2y.\left(2x^2-y\right)-2x^2.\left(2x^2y-y^2\right)\)
d.\(3x^2.\left(2y-1\right)-\left[2x^2.\left(5y-3\right)-2x.\left(x-1\right)\right]\)
e.\(4x\left(x^3-4x^2\right)+2x\left(2x^3-x^2+7x\right)\)
f.\(25x-4\left(3x-1\right)+7x\left(5-2x^2\right)\)
Bài 1: Tìm x biết:
a, \(x.\cdot\left(\frac{1}{4}+\frac{1}{5}\right)-\left(\frac{1}{7}+\frac{1}{8}\right)=0\)
b, \(\left(5x-1\right).\left(2x-\frac{1}{3}\right)=0\)
c, \(\frac{3x+2}{5x+7}=\frac{3x-1}{5x+1}\)
d, \(\frac{x+1}{2x+1}=\frac{0,5x+2}{x+3}\)
e, \(\frac{-3}{4}-\left|\frac{4}{5}-x\right|=-1\)
Tìm x, biết:
1) \(\left|4x\right|=3x+12\) 7) \(\left|5x\right|-3x-2=0\)
2) \(\left|2x+4\right|=2x-5\) 8) \(x-5x+\left|-2x\right|-3=0\)
3)\(\left|x+3\right|=3x-1\) 9) \(\left|3-x\right|+x^2-\left(4+x\right)x=0\)
4) \(\left|x-4\right|+3x=5\)
5)\(\left|x-5\right|=3x\)
6) \(\left|x+2\right|=2x-10\)
chứng minh biểu thức sau không thuộc vào y và x
a)A=\(x\left(2x+1\right)-x^2\left(x+2\right)+\left(x^3-x+3\right)\)
b)B=\(x\left(x^3+2x^2-3x+2\right)-\left(x^2+2x\right)x^2+3x\left(x-1\right)+x-12\)
Tìm x
\(\left(2x+3\right)^2-\left(5x-4\right)\left(5x+4\right)=\left(x+5\right)^2-\left(3x-1\right)\left(7x+2\right)-\left(x^2-1+1\right)\)
Rút gọn biểu thức:
a, \(\left(2x+1\right)^2+\left(2x-1\right)^2-2\left(1+2x\right)\left(2x-1\right)\)
\(b,\left(x-1\right)^3-\left(x+2\right)\left(x^2-2x+4\right)+3\left(x-1\right)\left(x+1\right)\)
Rút gọn biểu thức:
\(a,\left(x+2\right)\left(x-2\right)-\left(x-3\right)\left(x+1\right)\)
\(b,\left(x-5\right)\left(2x+3\right)-2x\left(x-3\right)+x+7\)
\(c,\left(a+b\right)^2-\left(a-b\right)^2\)
