Timf x:
x+1=(x+1)2
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\(\frac{x+1}{2}=\frac{8}{x+1}\Rightarrow\left(x+1\right)^2=8.2\)
=>(x+1)2=16
=>x+1=\(\sqrt{16}\)
=>x+1=4
=>x=3
\(\Leftrightarrow x^3+2x^2-3x-x^3-3x^2=-4\)
\(\Leftrightarrow x^2+3x-4=0\)
=>(x+4)(x-1)=0
=>x=-4 hoặc x=1
1) \(x:\dfrac{1}{3}=\dfrac{1}{2}+\dfrac{1}{3}\)
\(\Rightarrow3\times x=\dfrac{5}{6}\Rightarrow x=\dfrac{5}{18}\)
2) \(\left(x:\dfrac{2}{3}\right):\dfrac{2}{5}=\dfrac{7}{10}\)
\(\Rightarrow\dfrac{3}{2}\times x=\dfrac{7}{10}\times\dfrac{2}{5}=\dfrac{7}{25}\)
\(\Rightarrow x=\dfrac{7}{25}:\dfrac{3}{2}=\dfrac{14}{75}\)
\(x+\left(x+1\right)+\left(x+2\right)+...+19+20=20\)
\(\Leftrightarrow x+\left(x+1\right)+\left(x+2\right)+...+19=0\)
\(\Leftrightarrow\frac{x\left(19+x\right)}{2}=0\)
\(\Leftrightarrow x\left(x+19\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x+19=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-19\end{cases}}\)
Mà \(x\ne0\)nên \(x=-19\)
\(\Leftrightarrow x^2-2x+1-9x^2+36x-36=0\\ \Leftrightarrow-8x^2+34x-35=0\\ \Leftrightarrow8x^2-34x+35=0\\ \Leftrightarrow8x^2-20x-14x+35=0\\ \Leftrightarrow\left(2x-5\right)\left(4x-7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=\dfrac{7}{4}\end{matrix}\right.\)
Ta có :
\(\left(x+1\right)^2=x+1\)
\(\Rightarrow\left(x+1\right)^2-\left(x+1\right)=0\)
\(\Rightarrow\left(x+1\right)x=0\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=-1\\x=0\end{array}\right.\)
Vậy x = - 1 ; x = 0