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\(\left(x^3-x^2-5x+21\right):\left(x^2-4x+7\right)\)
\(=\left(x^3-4x^2+3x^2+7x-12x+21\right):\left(x^2-4x+7\right)\)
\(=\left[\left(x^3-4x^2+7x\right)+\left(3x^2-12x+21\right)\right]:\left(x^2-4x+7\right)\)
\(=\left[x\left(x^2-4x+7\right)+3\left(x^2-4x+7\right)\right]:\left(x^2-4x+7\right)\)
\(=\left[\left(x^2-4x+7\right)\left(x+3\right)\right]:\left(x^2-4x+7\right)\)
\(=x+3\)
\(\left(x^3-6x^2+9x+14\right):\left(x-7\right)\)
\(=\left(x^3-7x^2+x^2-7x-2x+14\right):\left(x-7\right)\)
\(=[x^2\left(x-7\right)+x\left(x-7\right)-2\left(x-7\right)]:\left(x-7\right)\)
\(=\left(x-7\right)\left(x^2+x-2\right):\left(x-7\right)\)
\(=x^2+x-2\)
Bài 1:
a: x^3-6x^2+12x-7=0
=>x^3-x^2-5x^2+5x+7x-7=0
=>(x-1)(x^2-5x+7)=0
=>x=1
b: \(x\left(4x-5\right)-\left(2x+1\right)^2=0\)
=>4x^2-5x-4x^2-4x-1=0
=>-9x-1=0
=>9x+1=0
=>x=-1/9
a)4x3y-6xy2
=2xy(2x2-3y)
b)4x2-4x+1
=(2x)2-2*2x*1+12
=(2x-1)2
c)x2-2xy-3x+6y
=x(x-2y)-3(x-2y)
=(x-3)(x-2y)
d)x3-2x2+x-xy2
=x(x2-2x+1-y2)
=x[(x-1)2-y2]
=x(x-y-1)(x+y-1)
e)x2-x+y2-y-x2y2+xy
=xy2-x+y2-y-x2y2+x2-xy2+xy
=(xy2-x+y2-y)-x(xy2-x+y2-y)
=(1-x)(xy2-x+y2-y)
=(1-x)[xy2+xy+y2-(xy+y+x)]
=(1-x)[y(xy+y+x)-(xy+y+x)]
=(1-x)(y-1)(xy+y+x)
Bài 2:
a)x(x-y)+y(y-x)
=x2-xy+y2-xy
=(x-y)2.Tại x=53 và y=3 ta có:
N=(53-3)2=502=2500
b) x2013-53x2012+103x2011-51x2010
=x2010(x3-53x2+103x-51)
=x2010[x3-2x2+x-51x2+102x-51]
=x2010[x(x2-2x+1)-51(x2-2x+1)]
=x2010(x-51)(x2-2x+1).Tại x=51 ta có:
M=512010(51-51)(512-2*51+1)=0
Bài 1 :
a ) \(x^2-6x-y^2+9=\left(x^2-6x+9\right)-y^2=\left(x-3\right)^2-y^2=\left(x-3+y\right)\left(x-3-y\right)\)
b) \(25-4x^2-4xy-y^2=5^2-\left(4x^2+4xy+y^2\right)=5^2-\left(2x+y\right)^2=\left(5+2x+y\right)\left(5-2x-y\right)\)
c) \(x^2+2xy+y^2-xz-yz=\left(x+y\right)^2-z.\left(x+y\right)=\left(x+y\right)\left(x+y-z\right)\)
d) \(x^2-4xy+4y^2-z^2+4tz-4t^2=\left(x^2-4xy+4y^2\right)-\left(z^2-4tz+4t^2\right)\)
\(=\left(x-2y\right)^2-\left(z-2t\right)^2=\left(x-2y+z-2t\right).\left(x-2y-z+2t\right)\)
BÀi 2 :
a) \(ax^2+cx^2-ay+ay^2-cy+cy^2=\left(ax^2+cx^2\right)-\left(ay+cy\right)+\left(ay^2+cy^2\right)\)
\(=x^2.\left(a+c\right)-y\left(a+c\right)+y^2.\left(a+c\right)=\left(a+c\right).\left(x^2-y+y^2\right)\)
b) \(ax^2+ay^2-bx^2-by^2+b-a=\left(ax^2-bx^2\right)+\left(ay^2-by^2\right)-\left(a-b\right)\)
\(=x^2.\left(a-b\right)+y^2.\left(a-b\right)-\left(a-b\right)=\left(a-b\right)\left(x^2+y^2-1\right)\)
c) \(ac^2-ad-bc^2+cd+bd-c^3=\left(ac^2-ad\right)+\left(cd+bd\right)-\left(bc^2+c^3\right)\)
\(=-a.\left(d-c^2\right)+d.\left(b+c\right)-c^2.\left(b+c\right)=\left(b+c\right).\left(d-c^2\right)-a\left(d-c^2\right)\)
\(=\left(b+c-a\right)\left(d-c^2\right)\)
BÀi 3 :
a) \(x.\left(x-5\right)-4x+20=0\) \(\Leftrightarrow x\left(x-5\right)-4\left(x-5\right)=0\) \(\Leftrightarrow\left(x-5\right)\left(x-4\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}x-5=0\\x-4=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=5\\x=4\end{cases}}}\)
b) \(x.\left(x+6\right)-7x-42=0\)\(\Leftrightarrow x.\left(x+6\right)-7.\left(x+6\right)=0\) \(\Leftrightarrow\left(x+6\right)\left(x-7\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}x+6=0\\x-7=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=-6\\x=7\end{cases}}}\)
c) \(x^3-5x^2+x-5=0\) \(\Leftrightarrow x^2.\left(x-5\right)+\left(x-5\right)=0\) \(\Leftrightarrow\left(x-5\right)\left(x^2+1\right)\)
\(\Leftrightarrow\hept{\begin{cases}x^2+1=0\\x-5=0\end{cases}\Leftrightarrow\hept{\begin{cases}x^2=-1\left(KTM\right)\\x=5\end{cases}}}\)
d) \(x^4-2x^3+10x^2-20x=0\) \(\Leftrightarrow x.\left(x^3-2x^2+10x-20\right)=0\)\(\Leftrightarrow x.\left[x^2.\left(x-2\right)+10.\left(x-2\right)\right]=0\) \(\Leftrightarrow x.\left(x-2\right)\left(x^2+10=0\right)\)
\(\Leftrightarrow\hept{\begin{cases}x=0\\x-2=0\\x^2+10=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=0\\x=2\\x^2=-10\left(KTM\right)\end{cases}}}\)
a) \(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2\)
\(=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x-y\right)\left(x^2+xy+y^2\right)\left(x^2-xy+y^2\right)\)
b) sửa đề nhé!
\(6x-9-x^2=-\left(x^2-6x+9\right)\)
\(=-\left(x-3\right)^2\)
a ) -36a2 + x2 + 4y2 - 4xy
= ( x2 - 4xy + 4y2 ) - (6a)2
= ( x -2y )2 - (6a)2
= ( x - 2y - 6a ).(x - 2y + 6a )
b ) 10ax - 5ay +2x - y
= ( 10ax - 5ay ) + ( 2x - y )
= 5a ( 2x - y ) + ( 2x - y )
= ( 2x - y ) . (5a + 1 )
c ) 2a2b(x + y) - 4ab2(-x - y )
= 2a2b( x+ y ) + 4ab2(x + y )
= 2ab(x + y ) ( a + 2b )
a, \(-36a^2+x^2+4y^2-4xy=\left(x+2y\right)^2-\left(6a\right)^2=\left(x+2y-6a\right)\left(x+2y+6a\right)\)
b, \(10ax-5ay+2x-y=5a\left(2x-y\right)+2x-y=\left(5a+1\right)\left(2x-y\right)\)
c, \(2a^2b\left(x+y\right)-4ab^2\left(-x-y\right)=2a^2b\left(x+y\right)+4ab^2\left(x+y\right)\)
\(=\left(2a^2b+4ab^2\right)\left(x+y\right)=2ab\left(a+2b\right)\left(x+y\right)\)