a, \(x\left(x-1\right)\left(x+2\right)-x^3=x-\left(x-1\right)\)
\(\Rightarrow x\left(x^2+2x-x-2\right)-x^3=x-x+1\)
\(\Rightarrow x^3+x^2-2x-x^3=1\)
\(\Rightarrow x^2-2x-1=0\)
\(\Rightarrow x^2-2x+1-2=0\)
\(\Rightarrow\left(x-1\right)^2=2\)
\(\Rightarrow\left\{{}\begin{matrix}x-1=-\sqrt{2}\\x-1=\sqrt{2}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-\sqrt{2}+1\\x=\sqrt{2}+1\end{matrix}\right.\)
b, \(\left(x-5\right)\left(x+5\right)=x-5\)
\(\Rightarrow x^2-25-x+5=0\)
\(\Rightarrow x^2-5x+4x-20=0\)
\(\Rightarrow x\left(x-5\right)+4\left(x-5\right)=0\Rightarrow\left(x-5\right)\left(x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-5=0\\x+4=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=-4\end{matrix}\right.\)
Chúc bạn học tốt!!!
a)\(x\left(x-1\right)\left(x+2\right)-x^3=x-\left(x-1\right)\)
=>\(x\left(x^2+x-2\right)-x^3=x-x+1\)
=>\(x^3+x^2-2x-x^3=1\)
=>\(\left(x^2-2x+1\right)=2\)
=>\(\left(x-1\right)^2=2\)
=>\(x-1=-\sqrt{2}\) hoặc \(x-1=\sqrt{2}\)
=>\(x=1-\sqrt{2}\) hoặc \(x=1+\sqrt{2}\)
Vậy...
b)\(\left(x-5\right)\left(x+5\right)=x-5\)
=>\(x^2-25-x+5=0\)
=>\(x^2-x-20=0\)
=>\(\left(x-5\right)\left(x+4\right)=0\)
=>\(x-5=0\) hoặc \(x+4=0\)
=>\(x=5\)hoặc \(x=-4\)
Vậy...
