a: \(x^2-4=0\)
=>\(x^2=4\)
=>\(\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
b: \(\left(x-1\right)^2-2\left(x-1\right)=0\)
=>(x-1)(x-1-2)=0
=>(x-1)(x-3)=0
=>\(\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
c: \(16x^2-9=0\)
=>\(16x^2=9\)
=>\(x^2=\dfrac{9}{16}\)
=>\(\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=-\dfrac{3}{4}\end{matrix}\right.\)
d: \(\left(x+2\right)^2-\left(x-3\right)\left(x+3\right)=32\)
=>\(x^2+4x+4-\left(x^2-9\right)=32\)
=>4x+13=32
=>4x=32-13=19
=>\(x=\dfrac{19}{4}\)
e: \(\left(x-1\right)^2-x^2-4x-4=0\)
=>\(x^2-2x+1-x^2-4x-4=0\)
=>-6x-3=0
=>-6x=3
=>\(x=-\dfrac{3}{6}=-\dfrac{1}{2}\)
f: \(\left(2x+1\right)^2-4\left(x-1\right)\left(x+1\right)=0\)
=>\(4x^2+4x+1-4\left(x^2-1\right)=0\)
=>\(4x^2+4x+1-4x^2+4=0\)
=>4x=-5
=>\(x=-\dfrac{5}{4}\)
`a, x^2 - 4=0`
`=> x^2=4`
`=>x^2=(+-2)^2`
`=> x=+-2`
Vậy: `x=+-2`
`b, (x-1)^2 - 2(x-1)=0`
`=> (x-1-2)(x-1)=0`
`=> (x-3)(x-1)=0`
`=> [(x-3=0),(x-1=0):}`
`=> [(x=3),(x=1):}`
Vậy: `x=3;x=1`
`c, 16x^2 - 9 = 0`
`=> 16x^2=9`
`=> x^2=9/16`
`=> x^2=(+-3/4)^2`
`=> x=+-3/4`
Vậy: `x=+-3/4`
`d, (x+2)^2 - (x-3)(x+3) = 32`
`=>(x+2)^2 - (x^2 - 9) = 32`
`=> x^2+4x+4-x^2+9=32`
`=> 4x+13=32`
`=> 4x=19`
`=> x=19/4`
Vậy: `x=19/4`