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Bài làm
a) \(\frac{x^4-2x^2+1}{x^3-3x-2}=\frac{\left(x^2-1\right)^2}{x^3-2x^2+2x^2-4x+x-2}\)
\(=\frac{\left[\left(x-1\right)\left(x+1\right)\right]^2}{x^2\left(x-2\right)+2x\left(x-2\right)+\left(x-2\right)}\)
\(=\frac{\left(x-1\right)^2\left(x+1\right)^2}{\left(x-2\right)\left(x^2+2x+1\right)}\)
\(=\frac{\left(x-1\right)^2\left(x+1\right)^2}{\left(x-2\right)\left(x+1\right)^2}=\frac{\left(x-1\right)^2}{x-2}\)
b) \(\frac{x^7+x^6+x^5+x^4+x^3+x^2+x+1}{x^4-1}\)
\(=\frac{\left(x^7+x^6\right)+\left(x^5+x^4\right)+\left(x^3+x^2\right)+\left(x+1\right)}{\left(x^2-1\right)\left(x^2+1\right)}\)
\(=\frac{x^6\left(x+1\right)+x^4\left(x+1\right)+x^2\left(x+1\right)+\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x^2+1\right)}\)
\(=\frac{\left(x+1\right)\left(x^6+x^4+x^2+1\right)}{\left(x-1\right)\left(x+1\right)\left(x^2+1\right)}\)
\(=\frac{x^6+x^4+x^2+1}{\left(x-1\right)\left(x^2+1\right)}\)
\(=\frac{\left(x^6+x^4\right)+\left(x^2+1\right)}{\left(x-1\right)\left(x^2+1\right)}\)
\(=\frac{x^4\left(x^2+1\right)+\left(x^2+1\right)}{\left(x-1\right)\left(x^2+1\right)}\)
\(=\frac{\left(x^2+1\right)\left(x^4+1\right)}{\left(x-1\right)\left(x^2+1\right)}=\frac{x^4+1}{x-1}\)
\(2x-x^2=0\)
\(x\left(2-x\right)=0\)
\(\Rightarrow\hept{\begin{cases}x=0\\2-x=0\end{cases}}\Rightarrow\hept{\begin{cases}x=0\\x=2\end{cases}}\)
Bài làm
Phân tích đa thức thành nhân tử
a) x2 + 7x + 12 = x2 + 3x + 4x + 12 = x( x + 3 ) + 4( x + 3 ) = ( x + 3 )( x + 4 )
b) 4x2 + 14x + 6 = 4x2 + 12x + 2x + 6 = 4x( x + 3 ) + 2( x + 3 ) = 2( x + 3 )( 2x + 1 )
4x2 + 2y2 + 2z2 - 4xy - 4xz + 2yz - 6y - 10z + 34 = 0
<=> ( 4x2 - 4xy + y2 - 4xz + 2yz + z2 ) + ( y2 - 6y + 9 ) + ( z2 - 10z + 25 ) = 0
<=> [ ( 4x2 - 4xy + y2 ) - ( 4xz - 2yz ) + z2 ] + ( y - 3 )2 + ( z - 5 )2 = 0
<=> [ ( 2x - y )2 - 2( 2x - y )z + z2 ] + ( y - 3 )2 + ( z - 5 )2 = 0
<=> ( 2x - y - z )2 + ( y - 3 )2 + ( z - 5 )2 = 0
<=> \(\hept{\begin{cases}2x-y-z=0\\y-3=0\\z-5=0\end{cases}}\Rightarrow\hept{\begin{cases}x=4\\y=3\\z=5\end{cases}}\)
=> S = ( x - 4 )2012 + ( y - 4 )2017 + ( z - 4 )1282
= ( 4 - 4 )2012 + ( 3 - 4 )2017 + ( 5 - 4 )1282
= 0 - 1 + 1 = 0
Thanks bn nhưng mik vừa làm xog r :)))))))))))))))))))))))))))
