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\(\left(x-1\right)^3-\left(3x-5\right)\left(3x+5\right)=\left(x-3\right)\left(x^2+3x+9\right)-3x\left(x-1\right)-9x^2+x\) \(\text{⇔}x^3-3x^2+3x-1-9x^2+25=x^3-27-3x^2+3x-9x^2+x\) \(\text{⇔}3x-4x+51=0\)
\(\text{⇔}x=51\)
KL.......
a) = x3 + 9x2 + 27x + 27 - 9x3 -6x2 - x + 8x3 +1 -3x2 =54
26x +28 = 54
26x = 54-28 = 26
x = 1
b) = x3 - 9x2 + 27x -27 - x3 +27 +6x2 + 12x + 6 +3x2 = -33
39x +6 = -33
39x = -33-6 = -39
x = -1
1) \(\left(3x+4\right)\left(3x-4\right)-\left(2x+5\right)^2=\left(x-5\right)^2+\left(2x+1\right)^2-\left(x^2-2x\right)+\left(x-1\right)^2\)
\(\Leftrightarrow9x^2-16-4x^2-20x-25=x^2-10x+25+4x^2+4x+1-x^2+2x+x^2-2x+1\)
\(\Leftrightarrow9x^2-4x^2-x^2-4x^2+x^2-x^2-20x+10x-4x-2x+2x=25+1+1+16+25\)
\(\Leftrightarrow-14x=68\)
\(\Leftrightarrow x=-\dfrac{34}{7}\)
Vậy................
2) \(\left(x-5\right)\left(x+5\right)-\left(x-2\right)^3-7x^2+\left(x+1\right)\left(x^2-x+1\right)=\left(x+3\right)^3-\left(x^3+9x^2\right)\)
\(=x^2-25-x^3+6x^2-12x+8-7x^2+x^3+1=x^3+9x^2+27x+27-x^3-9x^2\)
\(\Leftrightarrow x^2+6x^2-7x^2-9x^2+9x^2-x^3+x^3-x^3+x^3-12x-27x=27-1-8+25\)
\(\Leftrightarrow-39x=43\)
\(\Leftrightarrow x=-\dfrac{43}{39}\)
Vậy................
1. ( 3x + 4 )( 3x - 4 ) - ( 2x + 5 )2 = ( x - 5 )2 + ( 2x + 1 )2 - ( x2 - 2x ) + ( x - 1 )2
⇔ 9x2 - 16 - 4x2 - 20x - 25 = x2 - 10x + 25 + 4x2 + 4x + 1 - x2 + 2x + x2 - 2x + 1
⇔ - 18x - 68 = 0
⇔ -2( 9x + 34 ) = 0
⇔ x = \(\dfrac{34}{9}\)
KL.....................
2) ( x - 5 )( x + 5 ) - ( x - 2 )3 - 7x2 + ( x + 1 )( x2 - x + 1 ) = ( x + 3 )3 - ( x3 + 9x2 )
⇔ x2 - 25 - x3 + 6x2 - 12x + 8 - 7x2 + x3 + 1 = x3 + 9x2 + 27x + 27 - x3 - 9x2
⇔ - 39x- 43 = 0
⇔ 39x + 43 = 0
⇔ x =\(-\dfrac{43}{39}\)
KL...................
M = ( x + 4 )( x - 4 ) - 2x( 3 + x ) + ( x + 3 )2
= x2 - 16 - 6x - 2x2 + x2 + 6x + 9
= -7 ( đpcm )
N = ( x2 + 4 )( x + 2 )( x - 2 ) - ( x2 + 3 )( x2 - 3 )
= ( x2 + 4 )( x2 - 4 ) - ( x4 - 9 )
= x4 - 16 - x4 + 9
= -7 ( đpcm )
P = ( 3x - 2 )( 9x2 + 6x + 4 ) - 3( 9x3 - 2 )
= 27x3 - 8 - 27x3 + 6
= -2 ( đpcm )
Q = ( 3x + 2 )2 + ( 6x + 10 )( 2 - 3x ) + ( 2 - 3x )2
= 9x2 + 12x + 4 + 12x - 18x2 + 20 - 30x + 4 - 12x + 9x2
= -18x + 28 ( có phụ thuộc vào biến )
\(L=\left(2-3x\right)^3+2x\left(x-3\right)^2+\left(3x+1\right)\left(9x^2-3x+1\right)-6x\left(7x-3\right)+3x^3\)
\(=\left(8-36x+54x^2-27x^3\right)+2x\left(x^2-6x+9\right)+\left(27x^3+1\right)-42x^2+18x+3x^3\)
\(=8-36x+54x^2-27x^3+2x^3-12x^2+18x+27x^3+1-42x^2+18x+3x^3\)
\(=5x^3+9\)
=> biểu thức L phụ thuộc biến x => đề sai
\(\left(x+1\right)^3-\left(x+3\right)\left(x^2-3x+9\right)=\left(x-3\right)^3+3\left(2x+1\right)^2-\left(x^3-5x+1\right)\)
\(\Leftrightarrow x^3+3x^2+3x+1-x^3-27=x^3-9x^2+27x-27+12x^2+12x+3-x^3+5x-1\)
\(\Leftrightarrow3x^2+3x-26=3x^2+44x-25\)
\(\Leftrightarrow-41x=1\)
\(\Leftrightarrow x=-\dfrac{1}{41}\)
\(\Leftrightarrow x^3+3x^2+3x+1-x^3-27=\left(x-3\right)^3-x^3+5x-1+3\left(2x+1\right)^2\)
\(\Leftrightarrow3x^2+3x-26=x^3-9x^2+27x-27-x^3+5x-1+3\left(2x+1\right)^2\)
\(\Leftrightarrow3x^2+3x-26=-9x^2+32x-28+12x^2+12x+3\)
\(\Leftrightarrow3x^2+3x-26=3x^2+44x-25\)
=>-41x=1
hay x=-1/41
\(\left(x-1\right)^3-\left(3x-5\right)\left(3x+5\right)=\left(x-3\right)\left(x^2+3x+9\right)-3x\left(x-1\right)-9x^2+x\)
\(\Leftrightarrow x^3-3x^2+3x-1-9x^2+25=x^3-27-3x^2+3x-9x^2+x\)
\(\Leftrightarrow\left(x^3-x^3\right)+\left(-3x^2-9x^2+9x^2+3x^2\right)+\left(3x-3x-x\right)-1+25+27=0\)
\(\Leftrightarrow-x+51=0\)
\(\Leftrightarrow x=51\)
Vậy ,....