Question

Answer 1

a)\(\left(x-5\right)^2+3\left(x-5\right)=0\)

<=>\(\left(x-5\right)\left(x-5+3\right)\)=0

<=>\(\left(x-5\right)\left(x-2\right)\)=0

<=>x-5=0 hoặc x-2=0

<=>x=5 hoặc x=2

b)\(\dfrac{2x-1}{3}-\dfrac{5x+2}{7}=x+13\)

=>7(2x-1)-3(5x+2)=21(x+13)

<=>14x-7-15x-6=21x+273

<=>14x-15x-21x=273+7+6

<=>-22x=286

<=>x=-13

c)\(\dfrac{x-1}{x+2}-\dfrac{x}{x-2}=\dfrac{7x-6}{4-x^2}\)

<=>\(\dfrac{x-1}{x+2}-\dfrac{x}{x-2}=-\dfrac{7x+6}{x^2-4}\)

<=>(x-1)(x-2)-x(x+2)=-7x+6

<=>x²-2x-x+2-x²+2=-7x+6

<=>x²-x²-2x-x+7x=6+2+2

<=>4x=8

<=>x=2(ktm)

vô nghiệm

 

Answer 2

\(a,\left(x-5\right)^2+3\left(x-5\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(x-5+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x-2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=2\end{matrix}\right.\)

\(b,\dfrac{2x-1}{3}-\dfrac{5x+2}{7}=x+13\)

\(\Leftrightarrow7\left(2x-1\right)-3\left(5x+2\right)-21\left(x+13\right)=0\left(MSC:21\right)\)

\(\Leftrightarrow14x-7-15x-6-21x-273=0\)

\(\Leftrightarrow-22x=286\)

\(\Leftrightarrow x=-13\)

\(c,\dfrac{x-1}{x+2}-\dfrac{x}{x-2}=\dfrac{7x-6}{4-x^2}\left(dkxd:x\ne\pm2\right)\)

\(\Leftrightarrow\dfrac{x-1}{x+2}-\dfrac{x}{x-2}-\dfrac{7x-6}{4-x^2}=0\)

\(\Leftrightarrow\dfrac{x-1}{x+2}-\dfrac{x}{x-2}-\dfrac{7x-6}{x^2-4}=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)-x \left(x+2\right)-7x+6=0\)

\(\Leftrightarrow x^2-3x+2-x^2-2x-7x+6=0\)

\(\Leftrightarrow-12x=-8\)

\(\Leftrightarrow x=\dfrac{2}{3}\left(tmdk\right)\)

Answer 3

a) \(\left(x-5\right)^2+3\left(x-5\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left[\left(x-5\right)+3\right]=0\)

\(\Leftrightarrow\left(x-5\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-5=0\\x-2=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=5\\x=2\end{matrix}\right.\)

b) \(\dfrac{2x+1}{3}-\dfrac{5x+2}{7}=x+13\)

\(\Leftrightarrow\dfrac{7\left(2x-1\right)}{21}-\dfrac{3\left(5x+2\right)}{21}=\dfrac{21\left(x+13\right)}{21}\)

\(\Leftrightarrow7\left(2x-1\right)-3\left(5x+2\right)=21\left(x+13\right)\)

\(\Leftrightarrow14x-7-15x-6=21x+273\)

\(\Leftrightarrow14x-15x-21x=273+7+6\)

\(\Leftrightarrow-22x=286\)

\(\Leftrightarrow x=-\dfrac{286}{22}=-13\)

c) \(\dfrac{x-1}{x+2}-\dfrac{x}{x-2}=\dfrac{7x-6}{4-x^2}\)

\(\Leftrightarrow\dfrac{x-1}{x+2}-\dfrac{x}{x-2}=\dfrac{7x-6}{\left(x+2\right)\left(x-2\right)}\)

\(\Leftrightarrow\dfrac{\left(x-2\right)\left(x-1\right)}{\left(x+2\right)\left(x-2\right)}-\dfrac{x\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}=\dfrac{7x-6}{\left(x+2\right)\left(x-2\right)}\)

\(\Leftrightarrow\left(x-2\right)\left(x-1\right)-x\left(x+2\right)=7x-6\)

\(\Leftrightarrow x^2-x-2x+2-x^2+2x=7x-6\)

\(\Leftrightarrow-x+2=7x-6\)

\(\Leftrightarrow-x-7x=-6-2\)

\(\Leftrightarrow-8x=-8\)

\(\Leftrightarrow x=\dfrac{-8}{-8}=1\)