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\(\left(2x+1\right)^2\left(x-1\right)-2\left(x-2\right)^3+x\left(3-2x\right)\left(3+x\right)-\left(3x-3\right)^2\)
\(=\left(4x^2+4x+1\right)\left(x-1\right)-2\left(x^3-6x^2+12x-8\right)+x\left(9+3x-6x-2x^2\right)-\left(9x^2-18x+9\right)\)
\(=4x^3+4x^2+x-4x^2-4x-1-2x^3+12x^2-24x+16+9x+3x^2-6x^2-2x^3-9x^2+18x+9\)
\(=\left(4x^3-2x^2-2x^3\right)+\left(4x^2-4x^2+12x^2+3x^2-6x^2-9x^2\right)+\left(x-4x-24x+9x+18x\right)+\left(-1+16+9\right)\)
\(=24\)
Vậy...........
Chúc bạn học tốt!!!
1> 3x(x-2)-2x(2x-1)=(1-x)(1+x)
⇔\(3x^2\)-6x-\(4x^2\)+2x=1-\(x^2\)
⇔-1\(x^2\) - 4x= 1- \(x^2\)
⇔ -1\(x^2\) -4x+ \(x^2\) = 1
⇔-4x=1
⇔ x = \(\dfrac{-1}{4}\)
\(\left(2x+1\right)^3-\left(2x-1\right)^3-2\left(4x+3\right)^2+8\left(x+3\right)^2\)
\(=8x^3+12x^2+6x+1-\left(8x^3-12x^2+6x-1\right)-2\left(16x^2+24x+9\right)+8\left(x^2+6x+9\right)\)
\(=8x^3+12x^2+1-8x^3+12x^2-6x+1-32x^2-48x-18+8x^2+48x+72\)
\(=56\)
Chúc bạn học tốt!!!
\(1,\left(2x+1\right)^3-\left(2x-1\right)^3-2\left(4x+3\right)^2+8\left(x+3\right)^2\)\(=8x^3+12x^2+6x+1-8x^3+12x^2-6x+1-2\left(16x^2+24x+9\right)+8\left(x^2+6x+9\right)\)\(=8x^3+12x^2+6x+1-8x^3+12x^2-6x+1-32x^2-48x-18+8x^2+48x+72\)\(=56\)
vậy:.............
\(a,4x^2-\left(3x+1\right)\left(2x-1\right)=2\left(x-3\right)^2\)
\(\Leftrightarrow4x^2-\left(6x^2-3x+2x-1\right)=2\left(x^2-6x+9\right)\)
\(\Leftrightarrow4x^2-6x^2+x+1-2x^2+12x-18=0\)
\(\Leftrightarrow-4x^2+13x-17=0\)
\(\Leftrightarrow-4\left(x^2-\dfrac{13}{4}x+\dfrac{169}{64}\right)-\dfrac{103}{16}=0\)
\(\Leftrightarrow-4\left(x-\dfrac{13}{8}\right)^2=\dfrac{103}{16}\)
\(\Leftrightarrow\left(x-\dfrac{13}{8}\right)^2=\dfrac{-103}{64}\Rightarrow\) pt vô nghiệm
\(b,\left(5x-1\right)\left(x+1\right)-\left(2x-1\right)\left(2x+1\right)=x.\left(x+1\right)\)\(\Leftrightarrow5x^2+5x-x-1-\left(4x^2-1\right)=x^2+x\)
\(\Leftrightarrow5x^2+5x-x-1-4x^2+1-x^2-x=0\) \(\Leftrightarrow3x=0\Rightarrow x=0\)
\(c,7x^2-\left(2x-3\right)^2=1+3\left(x+2\right)^2\)
\(\Leftrightarrow7x^2-\left(4x^2-12x+9\right)=1+3\left(x^2+4x+4\right)\)
\(\Leftrightarrow7x^2-4x^2+12x-9=1+3x^2+12x+12\)\(\Leftrightarrow7x^2-4x^2+12x-9-1-3x^2-12x-12=0\)\(\Leftrightarrow-22=0\) ( vô lí)
Vậy phương trình vô nghiệm
1: \(=x^3-6x^2+12x-8-8x^3-36x^2-54x-27+7\left(x-1\right)^3\)
\(=-7x^3-42x^2-42x-35+7x^3-21x^2+21x-7\)
\(=-63x^2-21x-42\)
2: \(=x^3+125-\left(x^3-8\right)=125+8=133\)
3: \(=8x^3-27-8x^3-12x^2-6x-1=-12x^2-6x-28\)
1. (2x - 3) . (2x+3) - 4 . (x+ 2)2 = 6
[ ( 2x )2 - 32 ] - 4 . ( x2 + 2.x.2 + 22) = 6
4x2 - 9 - 4 . ( x2 + 4x + 4) = 6
4x2 - 9 - 4x2 - 16x - 16 = 6
-16x -25 = 6
x = \(-\dfrac{31}{16}\)
a)\((x^2- 4).(x^2 - 10) = 72 Đặt x^2 - 7 = a(1), ta có (a+3)(a-3)=72 a^2-9=72 a^2=81 a=+-9 xét 2 trường hợp a = 9 và -9 khi thay vào (1) ta có..... tự lm nốt nha \)
b) nhóm x+1 vs x+4 và x+2 vs x+3 ta sẽ có (x2+5x+4)(x2+5x+6)(x+5)=40
1: \(=8x^3+12x^2+6x+1-8x^3+12x^2-6x+1-2\left(4x+3\right)^2+8\left(x+3\right)^2\)
\(=24x^2+2-2\left(16x^2+24x+9\right)+8\left(x^2+6x+9\right)\)
\(=24x^2+2-32x^2-48x-18+8x^2+48x+72\)
=56
2: \(=\left(4x^2+4x+1\right)\left(x-1\right)-2\left(x^3-6x^2+12x-8\right)+x\left(3-2x\right)\left(3+x\right)-\left(3x-3\right)^2\)
\(=4x^3-3x-1-2x^3+12x^2-24x+16+x\left(9-3x-2x^2\right)-\left(3x-3\right)^2\)
\(=2x^3+12x^2-27x+15+9x-3x^2-2x^3-9x^2+18x-9\)
\(=6\)