Đáp án:
$3)
a) {\left[\begin{aligned}x=0\\x=25\end{aligned}\right.}\\
b) x=\dfrac{-25}{13}\\
c) {\left[\begin{aligned}x=1\\x=\dfrac{4}{3}\end{aligned}\right.}\\
d) {\left[\begin{aligned}x=3\\x=\dfrac{-1}{8}\end{aligned}\right.}\\$
Giải thích các bước giải:
$3)
a) x^2-25x=0\\
\Leftrightarrow x(x-25)=0\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x-25=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x=25\end{aligned}\right.}\\
b) x(3-x)+(x+5)^2=0\\
\Leftrightarrow 3x-x^2+x^2+10x+25=0\\
\Leftrightarrow 13x+25=0\\
\Leftrightarrow 13x=-25\\
\Leftrightarrow x=\dfrac{-25}{13}\\
c) 3x^2-7x+4=0\\
\Leftrightarrow 3x^2-3x-4x+4=0\\
\Leftrightarrow 3x(x-1)-4(x-1)=0\\
\Leftrightarrow (x-1)(3x-4)=0\\
\Leftrightarrow {\left[\begin{aligned}x-1=0\\3x-4=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=1\\3x=4\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=1\\x=\dfrac{4}{3}\end{aligned}\right.}\\
d) -8x^2+23x+3=0\\
\Leftrightarrow -(8x^2-23x-3)=0\\
\Leftrightarrow -(8x^2-24x+x-3)=0\\
\Leftrightarrow -[8x(x-3)+(x-3)]=0\\
\Leftrightarrow -(x-3)(8x+1)=0\\
\Leftrightarrow {\left[\begin{aligned}x-3=0\\8x+1=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=3\\x=\dfrac{-1}{8}\end{aligned}\right.}\\$
