Bài 1
1.(x-3)(x+2)-x(x-7)=15
\(\Leftrightarrow x^2+2x-3x-6-x^2+7x=15\)
\(\Leftrightarrow-6+6x=15\)
\(\Leftrightarrow6x=15+6\) =21
\(\Rightarrow x=\dfrac{21}{6}=3,5\)
2.(x-5)(x+5)+x(3-x)=20
\(\Leftrightarrow x^2-25+3x-x^2=20\)
\(\Leftrightarrow-25+3x=20\)
\(\Leftrightarrow3x=20+25=45\)
\(\Rightarrow x=\dfrac{45}{3}=15\)
3.(x-7)2-x(2+x)=-7
\(\Leftrightarrow x^2-14x+49-2x-x^2=-7\)
\(\Leftrightarrow-16x+49=-7\)
\(\Leftrightarrow-16x=-7-49=-56\)
\(\Rightarrow x=\dfrac{-56}{-16}=\dfrac{7}{2}=3,5\)
Tiếp bài 1
4.(x-4)2-(x+4)(x-4)=-16
\(\Leftrightarrow x^2-8x+16-x^2-16=-16\)
\(\Leftrightarrow-8x=-16\)
\(\Rightarrow x=\dfrac{-16}{-8}=2\)
5.(x-5)(x+5)-x(2-3x)=4x2-7
\(\Leftrightarrow x^2-25-2x+3x^2=4x^2-7\)
\(\Leftrightarrow4x^2-25-2x+3x^2=4x^2-7\)
\(\Leftrightarrow4x^2-4x^2-2x=-7+25\)
\(\Leftrightarrow-2x=18\)
\(\Rightarrow x=\dfrac{18}{-2}=-9\)
B2
1. 2x(x-2)+3x-6=0
=>2x(x-2)+3(x-2)=0
=>(x-2)(2x+3)=0
\(\Rightarrow\left[{}\begin{matrix}x-2=0\Leftrightarrow x=2\\2x+3=0\Leftrightarrow x=\dfrac{-3}{2}\end{matrix}\right.\)
2.3x(x-5)-5x+25=0
=>3x(x-5)-5(x-5)=0
=>(x-5)(3x-5)=0
\(\Rightarrow\left[{}\begin{matrix}x-5=0\Leftrightarrow x=5\\3x-5=0\Leftrightarrow x=\dfrac{5}{3}\end{matrix}\right.\)
3. x(x+7)-x-7=0
=>x(x+7)-(x+7)=0
=>(x+7)(x-1)=0
\(\Rightarrow\left[{}\begin{matrix}x+7=0\Leftrightarrow x=-7\\x-1=0\Leftrightarrow x=1\end{matrix}\right.\)
Bài 2)
a) 2x(x - 2) + 3x - 6 = 0
2x2 - 4x + 3x - 6 = 0
2x2 - x - 6 = 0
2x2 - 4x + 3x - 6 = 0
(2x2 - 4x) + (3x - 6) = 0
2x(x - 2) + 3(x - 2) = 0
(2x + 3)(x - 2) = 0
\(\Rightarrow\left\{{}\begin{matrix}2x+3=0\\x-2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=-3\\x=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{-3}{2}\\x=2\end{matrix}\right.\)
b) 3x(x - 5) - 5x + 25 = 0
3x(x - 5) - (5x - 25) = 0
3x(x - 5) - 5(x - 5) = 0
(3x - 5)(x - 5) = 0
\(\Rightarrow\left\{{}\begin{matrix}3x-5=0\\x-5=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3x=5\\x=5\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{5}{3}\\x=5\end{matrix}\right.\)
c) x(x + 7) -x - 7 = 0
x(x + 7) - (x + 7) = 0
(x - 1)(x + 7) = 0
\(\Rightarrow\left\{{}\begin{matrix}x-1=0\\x+7=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=1\\x=-7\end{matrix}\right.\)
d) (5x - 20) + 3x2 - 12x = 0
5(x - 4) + 3x(x - 4) = 0
(5 + 3x)(x - 4) = 0
\(\Rightarrow\left\{{}\begin{matrix}5+3x=0\\x-4=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3x=-5\\x=4\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{-5}{3}\\x=4\end{matrix}\right.\)
e) (1 - x) - 3x2 + 3x = 0
(1 - x) + (3x - 3x2) = 0
(1 - x) + 3x(1 - x) = 0
(1 - x)(1 + 3x) = 0
\(\Rightarrow\left\{{}\begin{matrix}1-x=0\\1+3x=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=1\\3x=-1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=1\\x=\dfrac{-1}{3}\end{matrix}\right.\)Chúc bn hok tốt