a, x\(^2\) - x = x - 1
\(\Leftrightarrow\) x\(^2\) - 2x + 1 = 0
\(\Leftrightarrow\) (x - 1)\(^2\) = 0
\(\Leftrightarrow\) x - 1 = 0
\(\Leftrightarrow\) x = 1
a) \(x^2-x=x-1\)
\(\Leftrightarrow x^2-2x+1=0\)
\(\Leftrightarrow\left(x-1\right)^2=0\)
\(\Rightarrow x=1\)
b) \(\left(x^2-36\right)-\left(x+6\right)=0\)
\(\Leftrightarrow\left(x+6\right)\left(x-7\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+6=0\\x-7=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=-6\\x=7\end{matrix}\right.\)
Vậy..
c) \(\left(2x-1\right)^2-\left(4x^2-1\right)=0\)
\(\Leftrightarrow4x^2-4x+1-4x^2+1=0\)
\(\Leftrightarrow-4x+2=0\)
\(\Rightarrow x=\dfrac{1}{2}\)
d) \(x^2\left(x^2-4\right)-\left(x^2-4\right)=0\)
\(\Leftrightarrow\left(x^2-4\right)\left(x^2-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x^2-4=0\\x^2-1=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=\pm2\\x=\pm1\end{matrix}\right.\)
Vậy..
a) x^2 - x = x - 1
\(x^2-x-\left(x-1\right)=0\)
\(x^2-2.x.1+1^2=0\)
\(\left(x-1\right)^2=0=>x-1=0=>x=1\)
b) (x^2 - 36) - (x+6) = 0
=> \(\left(x^2-6^2\right)-\left(x+6\right)=0\)
=> (x+6)(x-6) -(x+6) =0
=> (x-6)(x+6-1) =0
=> (x-6)(x+5)=0
=> x=6 hoặc x= (-5)
c) (2x-1)^2 - (4x^2 - 1)= 0
=> \(\left(2x-1\right)^2-\left(\left(2x\right)^2-1^2\right)=0\)
=>\(\left(2x-1\right)^2-\left(2x-1\right)\left(2x+1\right)=0\)
=> (2x-1)(2x-1-2x-1)=0
=> (2x-1)(-2)=0
=> 2x-1=0 => 2x=1 => x= \(\dfrac{1}{2}\)
d) x^2(x^2 - 4) - (x^2 - 4 ) = 0
\(\left(x^2-2^2\right)\left(x^2-1\right)=0\)
(x-2)(x+2)(x-1)(x+1)=0
=> x=2;-2;1 hoặc (-1)