[4+3x]2 = [4+3x]4
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\(P\left(x\right)=3x^4+9x^2-2x-3\)
\(Q\left(x\right)=\left(3x^4-3x^4\right)+\left(x^2-4x^2+1.5x^2\right)+2x+1=-1.5x^2+2x+1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(3x+4\right)^2+\left(5-3x\right)^2+2.\left(3x+4\right)\left(5-3x\right)\\ =\left[\left(3x+4\right)+\left(5-3x\right)\right]^2\\ =\left(3x+4+5-3x\right)^2\\ =9^2=81\)
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\(\left(3x-4\right)^2-2\left(3x-4\right)\left(x-4\right)+\left(4-x\right)^2\)
\(=\left(3x-4\right)^2+2\left(3x-4\right)\left(4-x\right)+\left(4-x\right)^2\)
\(=\left(3x-4+4-x\right)^2\)
\(=\left(2x\right)^2=4x^2\)
Ta có: \(\left(3x-4\right)^2-2\left(3x-4\right)\left(x-4\right)+\left(4-x\right)^2\)
\(=\left(3x-4+x-4\right)^2\)
\(=\left(4x-8\right)^2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(3x-4\right)^2+2\left(3x-4\right)\left(4-x\right)+\left(4-x\right)^2\)
\(=\left(3x-4+4-x\right)^2\)
\(=4x^2\)
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1: \(=6x^2+2x-15x-5-x^2+6x-9+4x^2+20x+25-27x^3-27x^2-9x-1\)
=-27x^3-18x^2+4x+10
2: =4x^2-1-6x^2-9x+4x+6-x^3+3x^2-3x+1+8x^3+36x^2+54x+27
=7x^3+37x^2+46x+33
5:
\(=25x^2-1-x^3-27-4x^2-16x-16-9x^2+24x-16+\left(2x-5\right)^3\)
\(=8x^3-60x^2+150-125+12x^2-x^3+8x-60\)
=7x^3-48x^2+8x-35
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1, 4[3x + 4] = 12x + 16
2, 4/3[5/3x + 6] = 20/9x + 12
3, [4/3x + 7]. 5 + 2 = 20/3x + 35 + 2 = 20/3x + 37
4, [3/7x - 6][-7] + 3x = -3x + 42 + 3x = 42
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a) ĐKXĐ : \(\left\{{}\begin{matrix}3x-2\ne0\\3x+2\ne0\\4-9x^2\ne0\end{matrix}\right.\Leftrightarrow x\ne\pm\dfrac{2}{3}\)
\(C=\dfrac{1}{3x-2}-\dfrac{4}{3x+2}-\dfrac{3x-6}{4-9x^2}\)
\(=\dfrac{3x+2}{\left(3x-2\right)\left(3x+2\right)}-\dfrac{4.\left(3x-2\right)}{\left(3x-2\right)\left(3x+2\right)}+\dfrac{3x-6}{9x^2-4}\)
\(=\dfrac{3x+2-4.\left(3x-2\right)+3x-6}{\left(3x-2\right).\left(3x+2\right)}=\dfrac{-6x+4}{\left(3x-2\right).\left(3x+2\right)}\)
\(=\dfrac{-2}{3x+2}\)
b) Với \(x\inℤ\)
Ta có : \(C\inℤ\Leftrightarrow-2⋮3x+2\)
\(\Leftrightarrow3x+2\inƯ\left(-2\right)\)
\(\Leftrightarrow3x+2\in\left\{1;2;-1;-2\right\}\)
Lập bảng
3x + 2 | 1 | 2 | -2 | -1 |
x | \(-\dfrac{1}{3}\left(\text{loại}\right)\) | 0(tm) | \(-\dfrac{4}{3}\left(\text{loại}\right)\) | -1(tm) |
Vậy \(x\in\left\{0;-1\right\}\)
Ta có :
Lập bảng
3x + 2 | 1 | 2 | -2 | -1 |
x | 0(tm) | -1(tm) |
Vậy
\(\left(4+3x\right)^2=\left(4+3x\right)^4\)
\(\Leftrightarrow1=\left(4x+3\right)^2\)
\(\Leftrightarrow\left(4+3x\right)^2=1\)
\(\Leftrightarrow\orbr{\begin{cases}4+3x=1\\4+3x=-1\end{cases}\Leftrightarrow}\orbr{\begin{cases}3x=-3\\3x=-5\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-1\\x=-\frac{5}{3}\end{cases}}\)
Vậy \(x=\left\{-1,\frac{-5}{3}\right\}\)