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29 tháng 12 2019
\(\frac{1}{\left(x+1\right)^2\left(x+2\right)}=\frac{a}{x+1}+\frac{b}{\left(x+1\right)^2}+\frac{c}{x+2}\)
\(=\frac{a}{x+1}+\frac{b}{x+1^2}+\frac{c}{x+2}\)
\(=\frac{1}{\left(x+1\right)^2\left(x+2\right)=}=\frac{a}{\left(x+1\right)\left(x+2\right)}+\frac{b}{x+2}+\frac{c}{\left(x+1\right)^2\left(x+2\right)}\)
\(\frac{c}{\left(x+1\right)^2}+\frac{a}{\left(x+1\right)\left(x+2\right)}+\frac{b}{\left(x+2\right)}=1\)
\(=\frac{c}{x^2+2c+x+1}+\frac{a}{x^2+3a\left(x+2a\right)}+\frac{b}{x+2b}=1\)
\(=\frac{\left(c+a\right)}{x^2+\left(2+x+1+\frac{a}{x^2+3ax+2a}+\frac{b}{x+2b}\right)=1}\)
\(=\frac{c+a}{x^2+\left(2c+3a+b\right)}x+2a+2b=0\)
\(\frac{c+a=0}{2c+3b=0}2a+2b=0\)
\(c=b=-a\)
Vậy:.....
8 tháng 8 2018
1) \(-6x^2-x+7=0\)
\(\Leftrightarrow-6x^2+6x-7x+7=0\)
\(\Leftrightarrow\left(-6x^2+6x\right)-\left(7x-7\right)=0\)
\(\Leftrightarrow-6x\left(x-1\right)-7\left(x-1\right)=0\)
\(\Leftrightarrow\left(-6x-7\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-6x-7=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{7}{6}\\x=1\end{matrix}\right.\)
2) \(-4x^2-5x+9=0\)
\(\Leftrightarrow-4x^2+4x-9x+9=0\)
\(\Leftrightarrow\left(-4x^2+4x\right)-\left(9x-9\right)=0\)
\(\Leftrightarrow-4x\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow\left(-4x-9\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-4x-9=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{9}{4}\\x=1\end{matrix}\right.\)
3) \(x^2+3x-4=0\)
\(\Leftrightarrow x^2-x+4x-4=0\)
\(\Leftrightarrow\left(x^2-x\right)+\left(4x-4\right)=0\)
\(\Leftrightarrow x\left(x-1\right)+4\left(x-1\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=1\end{matrix}\right.\)
4) \(x^2-6x-7=0\)
\(\Leftrightarrow x^2+x-7x-7=0\)
\(\Leftrightarrow\left(x^2+x\right)-\left(7x+7\right)=0\)
\(\Leftrightarrow x\left(x+1\right)-7\left(x+1\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=-1\end{matrix}\right.\)
5) \(x^2+5x+4=0\)
\(\Leftrightarrow x^2+x+4x+4=0\)
\(\Leftrightarrow\left(x^2+x\right)+\left(4x+4\right)=0\)
\(\Leftrightarrow x\left(x+1\right)+4\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+4\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-1\end{matrix}\right.\)
8 tháng 8 2018
a) \(-6x^2-x+7=0\)
\(\Leftrightarrow-6x^2+6x-7x+7=0\)
\(\Leftrightarrow-6x\left(x-1\right)-7\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(-6x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{-7}{6}\end{matrix}\right.\)
b) \(-4x^2-5x+9=0\)
\(\Leftrightarrow-4x^2+4x-9x+9=0\)
\(\Leftrightarrow-4x\left(x-1\right)-9\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(-4x-9\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2,25\end{matrix}\right.\)
c) \(x^2+3x-4=0\)
\(\Leftrightarrow x^2-x+4x-4=0\)
\(\Leftrightarrow x\left(x-1\right)+4\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-4\end{matrix}\right.\)
d) \(x^2-6x-7=0\)
\(\Leftrightarrow x^2+x-7x-7=0\)
\(\Leftrightarrow x\left(x+1\right)-7\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=7\end{matrix}\right.\)
e) \(x^2+5x+4=0\)
\(\Leftrightarrow x^2+x+4x+4=0\)
\(\Leftrightarrow x\left(x+1\right)+4\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-4\end{matrix}\right.\)
26 tháng 7 2018
1,\(x^4-x=0\\ ->x\left(x-1\right)\left(x^2+x+1\right)=0\\ ->\left(......\right)\)
2\(x^4-x^2=0\\ ->x^2\left(x^2-1\right)\\ ->x^2\left(x-1\right)\left(x+1\right)\\ ->......\)
3,\(x^5+x^2\\ ->x^2\left(x^3+1\right)\\ ->x^2\left(x+1\right)\left(x^2-x+1\right)\\ ->.......\)
4\(3x\left(x-20\right)-x+20=0->\left(3x-1\right)\left(x-20\right)=0->.....\)
A
0
21 tháng 8 2022
1: \(\Leftrightarrow3x+4x=4\)
=>7x=4
hay x=4/7
2: \(\Leftrightarrow3x-5x-5^3:5^2=0\)
=>-2x=5
=>x=-5/2
2 tháng 8 2018
A=26x2+y(2x+y)-10x(x+y)
A=26x2+2xy+y2-10x2-10xy
A=16x2-8xy+y2 =(4x)2-2.4x.y+y2 =(4x-y)2
Thay x=0,25y,ta có: A=(4.0,25y - y)2=(y-y)2=0
B=x3+6x2y+12xy2+8y3
B=x3+3x22y+3x(2y)2+(2y)3 =(x+2y)3
Có x+2y=-5 ⇒ x=-5-2y
Thay x=-5-2y vào, ta có B=(-5-2y+2y)3=(-5)3=-125
ND
1