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`a)2x^2+3(x-1)(x+1)=5x(x+1)`
`<=>2x^2+3x^2-3=5x^2+5x`
`<=>5x=-3`
`<=>x=-3/5`
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`b)(x-3)^3+3-x=0` nhỉ?
`<=>(x-3)^3-(x-3)=0`
`<=>(x-3)(x^2-1)=0`
`<=>[(x=3),(x^2=1<=>x=+-1):}`
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`c)5x(x-2000)-x+2000=0`
`<=>5x(x-2000)-(x-2000)=0`
`<=>(x-2000)(5x-1)=0`
`<=>[(x=2000),(x=1/5):}`
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`d)3(2x-3)+2(2-x)=-3`
`<=>6x-9+4-2x=-3`
`<=>4x=2`
`<=>x=1/2`
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`e)x+6x^2=0`
`<=>x(1+6x)=0`
`<=>[(x=0),(x=-1/6):}`
\(a,\Leftrightarrow9x^2=-36\Leftrightarrow x\in\varnothing\\ b,\Leftrightarrow3\left(x+4\right)-x\left(x+4\right)=0\\ \Leftrightarrow\left(3-x\right)\left(x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=-4\end{matrix}\right.\\ c,\Leftrightarrow2x^2-x-2x^2+3x+2=0\\ \Leftrightarrow2x=-2\Leftrightarrow x=-1\\ d,\Leftrightarrow\left(2x-3-2x\right)\left(2x-3+2x\right)=0\\ \Leftrightarrow-3\left(4x-3\right)=0\\ \Leftrightarrow x=\dfrac{3}{4}\\ e,\Leftrightarrow\dfrac{1}{3}x\left(x-9\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=9\end{matrix}\right.\\ f,\Leftrightarrow x^2\left(x-1\right)-\left(x-1\right)=0\\ \Leftrightarrow\left(x^2-1\right)\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)^2\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
\(a,\left(x+3\right).\left(x^2-3x+9\right)-\left(54+x^3\right)=x^3+27-54-x^3=-27.\)
\(b,8x^3+y^3-8x^3+y^3=2y^3\)
a ) ( 2x + 1 )2 - 4 ( x + 2 )2 = 9
4x2 + 4x + 1 - 4 ( x2 +4x + 4 ) = 9
4x2 + 4x + 1 - 4x2 -16x -16 = 9
-12x - 15 = 9
-12x = 24
x = -2
b) 3 ( x - 1 )2 - 3x ( x - 5 ) = 1
3 ( x2 - 2x + 1 ) - 3x2 + 15x = 1
3x2 - 6x + 3 - 3x2 + 15x = 1
9x + 3 = 1
9x = -2
x = \(\frac{-2}{9}\)
Bài 1:
- a,(2+xy)^2=4+4xy+x^2y^2
- b,(5-3x)^2=25-30x+9x^2
- d,(5x-1)^3=125x^3 - 75x^2 + 15x^2 - 1
m) \(\dfrac{1}{4}x^2-4x^2=\left(\dfrac{1}{2}x-2x\right)\left(\dfrac{1}{2}x+2x\right)\)
n) \(\dfrac{4}{49}-4x^2=\left(\dfrac{2}{7}-2x\right)\left(\dfrac{2}{7}+2x\right)\)
o) \(\left(x-3\right)\left(x+3\right)=x^2-9\)
Phân tích thôi hả :v
( 3x - 7 )2 - 25 = ( 3x - 7 )2 - 52 = ( 3x - 7 - 5 )( 3x - 7 + 5 ) = ( 3x - 12 )( 3x - 2 ) = 3( x - 4 )( 3x - 2 )
( x - 1/2 )2 - 9/4 = ( x - 1/2 )2 - ( 3/2 )2 = ( x - 1/2 - 3/2 )( x - 1/2 + 3/2 ) = ( x - 2 )( x + 1 )
49 - ( x + 7 )2 = 72 - ( x + 7 )2 = [ 7 - ( x + 7 ) ][ 7 + ( x + 7 ) ] = ( 7 - x - 7 )( 7 + x + 7 ) = -x( x + 14 )
25 - ( x - 3 )2 = 52 - ( x - 3 )2 = [ 5 - ( x - 3 ) ][ 5 + ( x - 3 ) ] = ( 5 - x + 3 )( 5 + x - 3 ) = ( 8 - x )( x + 2 )
a: 2/(x-2)=3/(x+2)
=>3x-6=2x+4
=>x=10
b: (x-2)(x+5)=0
=>x-2=0 hoặc x+5=0
=>x=2 hoặc x=-5
c: 2(x+2)-x=4
=>2x+4-x=4
=>x=0
\(a,\dfrac{2}{x-2}=\dfrac{3}{x+2}\)
\(\Leftrightarrow\dfrac{2}{x-2}-\dfrac{3}{x+2}=0\)
\(\Leftrightarrow\dfrac{2\left(x+2\right)-3\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow2x+4-3x+6=0\)
\(\Leftrightarrow-x+10=0\)
\(\Leftrightarrow-x=-10\)
\(\Leftrightarrow x=10\)
\(b,\left(x-2\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-5\end{matrix}\right.\)
\(c,2\left(x+2\right)-x=4\)
\(\Leftrightarrow2x+4-x-4=0\)
\(\Leftrightarrow x=0\)