llàm giúp mấy câu thoy.-.
a ) \(\left(2x-5-x+7\right)\left(2x-5+x-7\right)=0\)
\(\left(x-2\right)\left(3x-12\right)=0\)
=> x = 2 và x = \(\dfrac{12}{3}=4\)
b ) .
\(\left(3x-1\right)^2-\left(\left(3x\right)^2-2^2\right)=0\)
<=> \(9x^2-6x+1-9x^2+4=0\)
<=> \(-6x+5=0\)
=> \(x=\dfrac{-5}{-6}=\dfrac{5}{6}\)
c ) .
\(2x\left(x^2-25\right)=0\)
<=> \(2x\left(x-5\right)\left(x+5\right)=0\)
=> x = 0 ; x = 5 và x = -5
d).
<=> \(5x\left(x-2015\right)-\left(x-2015\right)=0\)
<=> \(\left(x-2015\right)\left(5x-1\right)=0\)
=>\(\left\{{}\begin{matrix}x-2015=0\\5x-1=0\end{matrix}\right.\) => \(\left\{{}\begin{matrix}x=2-15\\x=\dfrac{1}{5}\end{matrix}\right.\)
e ) với câu c trùng nhé
f ) .
<=> \(\left(3x+1\right)^2-4^2=0\)
<=> \(\left(3x+1-4\right)\left(3x+1+4\right)=0\)
<=> \(\left(3x-3\right)\left(3x+5\right)=0\)
=> \(\left\{{}\begin{matrix}3x-3=0\\3x+5=0\end{matrix}\right.\) => \(\left\{{}\begin{matrix}x=\dfrac{3}{3}=1\\x=-\dfrac{5}{3}\end{matrix}\right.\)
g chắc nhầm dấu nếu k thì dùng denta hoặc cong thuc bac 2 =)
h ) .
<=> \(3x\left(x^2-4\right)=0\)
<=> \(3x\left(x-2\right)\left(x+2\right)=0\)
=> \(\left\{{}\begin{matrix}3x=0\\x-2=0\\x+2=0\end{matrix}\right.\) => \(\left\{{}\begin{matrix}x=0\\x=2\\x=-2\end{matrix}\right.\)
i ) .
<=> \(x^2-4x+4-1=0\)
<=> \(\left(x-2\right)^2-1^2=0\)
<=> \(\left(x-2-1\right)\left(x-2+1\right)=0\)
<=> \(\left(x-3\right)\left(x-1\right)=0\)
=> \(\left\{{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
\(a,\left(2x-5\right)^2-\left(x-7\right)^2=0\\ \Leftrightarrow\left(2x-5-x+7\right)\left(2x-5+x-7\right)=0\\ \Leftrightarrow\left(x+2\right)\left(3x-12\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x=4\end{matrix}\right.\)
\(b,\left(3x-1\right)^2-\left(3x+2\right)\left(3x-2\right)=2015\\ \Leftrightarrow9x^2-6x+1-9x^2+4=2015\\ \Leftrightarrow-6x+5=2015\\ \Leftrightarrow-6x=2010\\ \Leftrightarrow x=x=-335\)
\(c,2x^3-50x=0\\ \Leftrightarrow2x\left(x^2-25\right)=0\\ \Leftrightarrow x\left(x-5\right)\left(x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=5\\x=-5\end{matrix}\right.\)
\(d,5x\left(x-2015\right)-x+2015=0\\ \Leftrightarrow5x\left(x-2015\right)-\left(x-2015\right)=0\\ \Leftrightarrow\left(x-2015\right)\left(5x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-2015=0\\x=\dfrac{1}{5}\end{matrix}\right.\)
`e,` giống câu c
\(f,\left(3x+1\right)^2-16=0\\ \Leftrightarrow\left(3x+1-4\right)\left(3x+1+4\right)=0\\ \Leftrightarrow\left(3x-3\right)\left(3x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{5}{3}\end{matrix}\right.\)
\(g,x^2-4x+5=0\\ \Leftrightarrow\left(x^2-4x+4\right)+1=0\\ \Leftrightarrow\left(x-2\right)^2=-1\left(vô.lí\right)\)
\(3x^3-12x=0\\ \Leftrightarrow3x\left(x^2-4\right)=0\\ \Leftrightarrow x\left(x-2\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\\x=2\end{matrix}\right.\)
\(i,x^2-4x+3=0\\ \Leftrightarrow x^2-x-3x+3=0\\ \Leftrightarrow x\left(x-1\right)-3\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
