Đáp án+Giải thích các bước giải:
11,
$x^2-5x=-6$
$⇔x^2-5x+6=0$
$⇔x^2-2x-3x+6=0$
$⇔x(x-2)-3(x-2)=0$
$⇔(x-3)(x-2)=0$
$⇔\left[\begin{matrix}x-3=0\\x-2=0\end{matrix}\right.$
$⇔\left[\begin{matrix}x=3\\x=2\end{matrix}\right.$
Vậy `S={3;2}`
12,
$x^2=4x-4(x≥1)$
$⇔x^2-4x+4=0$
$⇔(x-2)^2=0$
$⇔x-2=0$
$⇔x=2(t/m)$
Vậy `S={2}`
13,
$x^2=3x-2$
$⇔x^2-3x+2=0$
$⇔x^2-2x-x+2=0$
$⇔x(x-2)-(x-2)=0$
$⇔(x-1)(x-2)=0$
$⇔\left[\begin{matrix}x-1=0\\x-2=0\end{matrix}\right.$
$⇔\left[\begin{matrix}x=1\\x=2\end{matrix}\right.$
Vậy `S={1;2}`
14,
$x^3-3x^2+3x-1=0$
$⇔(x-1)^3=0$
$⇔x-1=0$
$⇔x=1$
Vậy `S={1}`
15,
$(2x-3)^2=(x+5)^2$
$⇔\left[\begin{matrix}2x-3=x+5\\2x-3=-x-5\end{matrix}\right.$
$⇔\left[\begin{matrix}x=8\\x=\dfrac{-2}{3}\end{matrix}\right.$
Vậy `S={\frac{-2}{3};8}`
