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a) (x-2)3+6(x+1)2-x3+12=0
\(\Rightarrow\)x3-6x2+12x-8+6(x2+2x+1)-x3+12=0
\(\Rightarrow\)x3-6x2+12x-8+6x2+12x+6-x3+12=0
\(\Rightarrow\)24x+10=0
\(\Rightarrow\)24x=-10
\(\Rightarrow\)x=\(\dfrac{-10}{24}=\dfrac{-5}{12}\)
b)(x-5)(x+5)-(x+3)2+3(x-2)2=(x+1)2-(x-4)(x+4)+3x2
\(\Rightarrow\)x2-25-(x2+6x+9)+3(x2-4x+4)=x2+2x+1-(x2-16)+3x2
\(\Rightarrow\)x2-25-x2-6x-9+3x2-12x+12=x2+2x+1-x2+16+3x2
\(\Rightarrow\)3x2-18x-22=3x2+2x+17
\(\Rightarrow\)3x2-18x-22-3x2-2x-17=0
\(\Rightarrow\)-20x-39=0
\(\Rightarrow\)-20x=39
\(\Rightarrow\)x=\(-\dfrac{39}{20}\)
a) ( x - 3 )( x + 3 )( x + 2 ) - ( x - 1 )( x2 - 3 ) - 5x( x + 4 )2 - ( x - 5 )2
= ( x2 - 32 )( x + 2 ) - ( x3 - x2 - 3x + 3 ) - 5x( x2 + 8x + 16 ) - ( x2 - 10x + 25 )
= x3 + 2x2 - 9x - 18 - x3 + x2 + 3x - 3 - 5x3 - 40x2 - 80x - x2 + 10x - 25
= ( x3 - x3 - 5x3 ) + ( 2x2 + x2 - 40x2 - x2 ) + ( -9x + 3x + 10x - 80x ) + ( -18 - 3 - 25 )
= -5x3 - 38x2 - 76x - 46
b) 2x( x - 4 )2 - ( x + 5 )( x - 2 )( x + 2 ) + 2( x + 5 )2 - ( x - 1 )2
= 2x( x2 - 8x + 16 ) - ( x + 5 )( x2 - 4 ) + 2( x2 + 10x + 25 ) - ( x2 - 2x + 1 )
= 2x3 - 16x2 + 32x - ( x3 + 5x2 - 4x - 20 ) + 2x2 + 20x + 50 - x2 + 2x - 1
= 2x3 - 16x2 + 32x - x3 - 5x2 + 4x + 20 + 2x2 + 20x + 50 - x2 + 2x - 1
= ( 2x3 - x3 ) + ( -16x2 - 5x2 + 2x2 - x2 ) + ( 32x + 4x + 20x + 2x ) + ( 20 + 50 - 1 )
= x3 - 20x2 + 58x + 69
c) ( x + 5 )2 - 4x( 2x + 3 )2 - ( 2x - 1 )( x + 3 )( x - 3 )
= x2 + 10x + 25 - 4x( 4x2 + 12x + 9 ) - ( 2x - 1 )( x2 - 9 )
= x2 + 10x + 25 - 16x3 - 48x2 - 36x - ( 2x3 - x2 - 18x + 9 )
= x2 + 10x + 25 - 16x3 - 48x2 - 36x - 2x3 + x2 + 18x - 9
= ( -16x3 - 2x3 ) + ( x2 - 48x2 + x2 ) + ( 10x - 36x + 18x ) + ( 25 - 9 )
= -18x3 - 46x2 - 8x + 16
d) -2x( 3x + 2 )( 3x - 2 ) + 5( x + 2 )2 - ( x - 1 )( 2x + 1 )( 2x - 1 )
= -2x( 9x2 - 4 ) + 5( x2 + 4x + 4 ) - ( x - 1 )( 4x2 - 1 )
= -18x3 + 8x + 5x2 + 20x + 20 - ( 4x3 - 4x2 - x + 1 )
= -18x3 + 8x + 5x2 + 20x + 20 - 4x3 + 4x2 + x - 1
= ( -18x3 - 4x3 ) + ( 5x2 + 4x2 ) + ( 8x + 20x + x ) + ( 20 - 1 )
= -22x3 + 9x2 + 29x + 19
=\(\frac{1}{x+1}-\frac{1}{x+2}\)+\(\frac{1}{x+2}-\frac{1}{x+3}\)+\(\frac{1}{x+3}-\frac{1}{x+4}+\frac{1}{x+4}\)-\(\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+6}\)
=\(\frac{1}{x+1}-\frac{1}{x+6}\)
=\(\frac{x+6-x-1}{\left(x+1\right)\left(x+6\right)}\)
=\(\frac{5}{\left(x+1\right)\left(x+6\right)}\)
1: Ta có: \(x^2-2x+5-\left(x-7\right)\left(x+2\right)\)
\(=x^2-2x+5-x^2-2x+7x-14\)
\(=3x-9\)
2: Ta có: \(-5x\left(x-5\right)+\left(x-3\right)\left(x^2-7\right)\)
\(=-5x^2+25x+x^3-7x-3x^2+21\)
\(=x^3-8x^2+18x+21\)
3: Ta có: \(x\left(x^2-x-2\right)-\left(x+5\right)\left(x-1\right)\)
\(=x^3-x^2-2x-x^2-4x+5\)
\(=x^3-2x^2-6x+5\)
a: \(\dfrac{x+5}{x-1}+\dfrac{8}{x^2-4x+3}=\dfrac{x+1}{x-3}\)
=>(x+5)(x-3)+8=x^2-1
=>x^2+2x-15+8=x^2-1
=>2x-7=-1
=>x=3(loại)
b: \(\dfrac{x-4}{x-1}-\dfrac{x^2+3}{1-x^2}+\dfrac{5}{x+1}=0\)
=>(x-4)(x+1)+x^2+3+5(x-1)=0
=>x^2-3x-4+x^2+3+5x-5=0
=>2x^2+2x-6=0
=>x^2+x-3=0
=>\(x=\dfrac{-1\pm\sqrt{13}}{2}\)
e: =>x^2-2x+1+2x+2=5x+5
=>x^2+3=5x+5
=>x^2-5x-2=0
=>\(x=\dfrac{5\pm\sqrt{33}}{2}\)
g: (x-3)(x+4)*x=0
=>x=0 hoặc x-3=0 hoặc x+4=0
=>x=0;x=3;x=-4
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