Lời giải:
`1.`
`(2x+1)^(2)-2x(2x+3)=4`
`⇔4x^(2)+4x+1-4x^(2)-6x-4=0`
`⇔-2x-3=0`
`⇔x=-3/2`
Vậy `x=-3/2`
`2`.
`(x-3)(x+3)-(x-2)^2=1`
`⇔x^(2)-9-x^(2)+4x-4-1=0`
`⇔4x-14=0`
`⇔x=7/2`
Vậy `x=7/2`
`3`.
`(x-1)(x^(2)+x+1)-x(x^(2)+2)-4=0`
`⇔x^(3)-1-x^(3)-2x-4=0`
`⇔-2x-5=0`
`⇔x=-5/2`
Vậy `x=-5/2`
`4`. Cách 1 : Áp dụng HĐT số 3 : `a^(2)-b^2=(a-b)(a+b)`
`(2-x)^(2)-9=0`
`⇔(2-x)^(2)-3^2=0`
`⇔(2-x-3)(2-x+3)=0`
`⇔(-x-1)(5-x)=0`
$⇔\left[\begin{matrix}-x-1=0\\5-x=0\end{matrix}\right.$
$⇔\left[\begin{matrix}x=-1\\x=5\end{matrix}\right.$
Vậy `x∈{-1;5}`
Cách `2` : Chuyển vế.
`(2-x)^(2)-9=0`
`⇔(2-x)^2=9`
`⇔(2-x)^2=±3`
$⇔\left[\begin{matrix}2-x=3\\2-x=-3\end{matrix}\right.$
$⇔\left[\begin{matrix}x=-1\\x=5\end{matrix}\right.$
Vậy `x∈{-1;5}`
`5.`
`x(x-5)(x+5)-(x+2)(x^(2)-2x+4)=3`
`⇔x(x^(2)-25)-(x^(3)+8)=3`
`⇔x^(3)-25x-x^(3)-8-3=0`
`⇔-25x-11=0`
`⇔x=-11/25`
Vậy `x=-11/25`
