a: Đặt \(x-x^2=0\)
=>x(1-x)=0
=>\(\left[\begin{array}{l}x=0\\ 1-x=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=1\end{array}\right.\)
b: Đặt 1-5x=0
=>5x=1
=>\(x=\frac15\)
c: Đặt |2-x|-5=0
=>|x-2|=5
=>\(\left[\begin{array}{l}x-2=5\\ x-2=-5\end{array}\right.\Rightarrow\left[\begin{array}{l}x=7\\ x=-3\end{array}\right.\)
d: Đặt \(2x^2-5x+3=0\)
=>\(2x^2-2x-3x+3=0\)
=>(x-1)(2x-3)=0
=>\(\left[\begin{array}{l}x-1=0\\ 2x-3=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=1\\ x=\frac32\end{array}\right.\)
e: Đặt \(x^2-4x+5=0\)
=>\(x^2-4x+4+1=0\)
=>\(\left(x-2\right)^2+1=0\) (vô lý)
=>x∈∅
f: Đặt x(x-2)+x-2=0
=>(x-2)(x+1)=0
=>\(\left[\begin{array}{l}x-2=0\\ x+1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=2\\ x=-1\end{array}\right.\)
g: Đặt 5x(x-3)-x+3=0
=>5x(x-3)-(x-3)=0
=>(x-3)(5x-1)=0
=>\(\left[\begin{array}{l}x-3=0\\ 5x-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3\\ x=\frac15\end{array}\right.\)
h: Đặt \(x^3-\frac14x=0\)
=>\(x\left(x^2-\frac14\right)=0\)
=>\(x\left(x-\frac12\right)\left(x+\frac12\right)=0\)
=>\(\left[\begin{array}{l}x=0\\ x-\frac12=0\\ x+\frac12=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=\frac12\\ x=-\frac12\end{array}\right.\)
i: Đặt \(x^2\left(x-3\right)+12-4x=0\)
=>\(x^2\left(x-3\right)-4\left(x-3\right)=0\)
=>\(\left(x-3\right)\left(x^2-4\right)=0\)
=>(x-3)(x-2)(x+2)=0
=>\(\left[\begin{array}{l}x-3=0\\ x-2=0\\ x+2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3\\ x=2\\ x=-2\end{array}\right.\)
