Đáp án+Giải thích các bước giải:
1,
a,
$6x^2-20x$
$=2x(3x-10)$
b,
$25x+15x^2$
$=5x(5+3x)$
c,
$x^2-12x+36$
$=(x-6)^2$
d,
$x^2-100$
$=(x+10)(x-10)$
e,
$16x^2-25y^2$
$=(4x-5y)(4x+5y)$
2,
a,
$4x^2-20x=0$
$⇒4x(x-5)=0$
$⇒\left[\begin{matrix}x=0\\x-5=0\end{matrix}\right.$
$⇒\left[\begin{matrix}x=0\\x=5\end{matrix}\right.$
Vậy `S={0;5}`
b,
$x^2-16=0$
$⇒x^2=16$
$⇒x=±4$
Vậy `S={±4}`
c,
$25-x^2=0$
$⇒x^2=25$
$⇒x=±5$
Vậy `S={±5}`
d,
$(x-12)^2-36=0$
$⇒(x-12+6)(x-12-6)=0$
$⇒(x-6)(x-18)=0$
$⇒\left[\begin{matrix}x-6=0\\x-18=0\end{matrix}\right.$
$⇒\left[\begin{matrix}x=6\\x=18\end{matrix}\right.$
Vậy `S={6;18}`
e,
$100-(x+1)^2=0$
$⇒(x+1)^2=100$
$⇒\left[\begin{matrix}x+1=10\\x+1=-10\end{matrix}\right.$
$⇒\left[\begin{matrix}x=9\\x=-11\end{matrix}\right.$
Vậy `S={9;-11}`
