`1)4x^2+1=4x^2+4x+1-4x=(2x+1)^2-4x=(2x-2\sqrt{x}+1)(2x+2\sqrt{x}+1)` (với `x >= 0`)

  `->` Ko có đ/á

(Câu này mình nghĩ là `4x^4+1` chứ nhỉ?)

`2)4x^4+y^4=4x^4+4x^2y^2+y^4-4x^2y^2`

        `=(2x^2+y^2)-(2xy)^2`

        `=(2x^2-2xy+y^2)(2x^2+2xy+y^2)`

   `->bb C`

a. \(\left(2x^2+y\right)\left(2x^2-y\right)-4x^2+y^2=\left(2x^2\right)^2-y^2-4x^2+y^2\)

\(=4x^4-4x^2\)

b. \(\left(2x^2+y\right)^2-\left(2x^2-y^2\right)=4x^4+4x^2y+y^2-2x^2+y^2\)

\(=4x^4+4x^2y-2x^2+2y^2\)

c. \(\left(2x+1\right)\left(2x-1\right)-4x^2=\left(2x\right)^2-1^2-4x^2=4x^2-1-4x^2=-1\)

d. \(\left(2x^{3y}+y\right)^2-\left(y-2x^{3y}\right)^2\)

\(=\left(2x^{3y}+y+y-2x^{3y}\right)\left(2x^{3y}+y-y+2x^{3y}\right)\)

\(=2y.2.2x^{3y}=4y.2x^{3y}\)

a/ \(\left(2x+1\right)\left(2x-1\right)-4x^2=\left(2x\right)^2-1^2-4x^2\)

\(=4x^2-1-4x^2\)

b/ \(\left(2x^2+y\right)\left(2x^2-y\right)-4x^2+y^2\)

\(=\left(2x^2\right)^2-y^2-4x^2+y^2=4x^4-y^2-4x^2+y^2=4x^4-4x^2\)

c/ \(\left(2x^2+y\right)^2-\left(2x^2-y\right)^2\)

\(=\left(2x^2+y+2x^2-y\right)\left(2x^2+y-2x^2+y\right)\)

\(=4x^2\cdot2y=8x^2y\)

d/ \(\left(2x^3y+y\right)^2-\left(y-2x^3y\right)^2=\left(2x^3y+y\right)^2-\left(2x^3y-y\right)^2\)

\(=\left(2x^3y+y+2x^3y-y\right)\left(2x^3y+y-2x^3y+y\right)\)

\(=4x^3y\cdot2y=8x^3y^2\)

b) đặt x^2+2x+2=t => t>0

\(\frac{t-1}{t}+\frac{t}{t+1}=\frac{7}{6}\Leftrightarrow\frac{2t^2-1}{t^2+t}=\frac{7}{6}\Leftrightarrow12t^2-6=7t^2+7t\)

\(\Leftrightarrow5t^2-7t-6=0\Leftrightarrow5t\left(t-2\right)+3t-6=\left(t-2\right)\left(5t+3\right)\Rightarrow\left[\begin{matrix}t=2\\t=\frac{-3}{5}\left(loai\right)\end{matrix}\right.\)

với t=2

\(x^2+2x+2=2\Rightarrow x^2+2x=0\Rightarrow\left[\begin{matrix}x=0\\x=-2\end{matrix}\right.\)

(x + 2)² - 2x - 4 = 0

<=> (x + 2)² - 2(x + 2) = 0

<=> (x + 2)(x + 2 - 2) = 0

<=> x(x + 2) = 0

<=> \(\left[{}\begin{matrix}x=0\\x+2=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)

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

\(2+\frac{2x^2-8x}{2x^2+8x}+\frac{2x^2+7x+23}{2x^2+7x-4}=\frac{2x+5}{2x-1}\)

\(\Leftrightarrow2+\frac{2x\left(x-4\right)}{2x\left(x+4\right)}+\frac{2x^2+7x+23}{\left(2x-1\right)\left(x+4\right)}=\frac{2x+5}{2x-1}\)

\(\Leftrightarrow2+\frac{x-4}{x+4}+\frac{2x^2+7x+23}{\left(2x-1\right)\left(x+4\right)}-\frac{2x+5}{2x-1}=0\)

\(\Leftrightarrow\frac{2\left(x+4\right)\left(2x-1\right)}{\left(x+4\right)\left(2x-1\right)}+\frac{\left(x-4\right)\left(2x-1\right)}{\left(x+4\right)\left(2x-1\right)}+\frac{2x^2+7x+23}{\left(2x-1\right)\left(x+4\right)}-\frac{\left(2x+5\right)\left(x+4\right)}{\left(2x-1\right)\left(x+4\right)}=0\)

\(\Leftrightarrow\frac{2\left(x+4\right)\left(2x-1\right)+\left(x-4\right)\left(2x-1\right)+2x^2+7x+23-\left(2x+5\right)\left(x+4\right)}{\left(x+4\right)\left(2x-1\right)}=0\)

\(\Leftrightarrow2\left(x+4\right)\left(2x-1\right)+\left(x-4\right)\left(2x-1\right)+2x^2+7x+23-\left(2x+5\right)\left(x+4\right)=0\)

\(\Leftrightarrow2\left(2x^2+7x-4\right)+\left(2x^2-9x+4\right)+2x^2+7x+23-\left(2x^2+13x+20\right)=0\)

\(\Leftrightarrow4x^2+14x-8+2x^2-9x+4+2x^2+7x+23-2x^2-13x-20=0\)

\(\Leftrightarrow6x^2+7x-1=0\)

\(\Leftrightarrow6\left(x^2+2.\frac{7}{12}.x+\frac{49}{144}\right)-\frac{193}{144}=0\)

\(\Leftrightarrow\left(x+\frac{7}{12}\right)^2=\frac{\frac{193}{144}}{6}=\frac{193}{864}\)

Bạn tự làm nốt.

Tương tự với Cb.

Bài làm

Như đã nhắn là mình sẽ làm theo quan điểm của mình là 5/(x^2 - 1) nha

\(A=\left[\frac{3\left(x+2\right)}{2x^3+2x+2x^2+2}+\frac{2x^2-x-10}{2x^3-2-2x^2+2x}\right]:\left[\frac{5}{x^2-1}+\frac{3}{2x+2}-\frac{3}{2x-2}\right]\)

\(A=\left[\frac{3\left(x+2\right)}{2x^2\left(x+1\right)+2\left(x+1\right)}+\frac{2x^2+4x-5x-10}{\left(2x^3-2x^2\right)+\left(2x-2\right)}\right]:\left[\frac{5}{x^2-1}+\frac{3}{2\left(x+1\right)}-\frac{3}{2\left(x-1\right)}\right]\)

\(A=\left[\frac{3\left(x+2\right)}{\left(2x^2+2\right)\left(x+1\right)}+\frac{2x\left(x+2\right)-5\left(x+2\right)}{2x^2\left(x-1\right)+2\left(x-1\right)}\right]:\left[\frac{5\cdot2}{2\left(x+1\right)\left(x-1\right)}+\frac{3}{2\left(x+1\right)}-\frac{3}{2\left(x-1\right)}\right]\)

\(A=\left[\frac{3\left(x+2\right)}{\left(2x^2+2\right)\left(x+1\right)}+\frac{\left(2x-5\right)\left(x+2\right)}{\left(2x^2+2\right)\left(x-1\right)}\right]:\left[\frac{5\cdot2}{2\left(x+1\right)\left(x-1\right)}+\frac{3}{2\left(x+1\right)}-\frac{3}{2\left(x-1\right)}\right]\)

\(A=\left[\frac{3\left(x+2\right)\left(x-1\right)}{\left(2x^2+2\right)\left(x^2-1\right)}+\frac{\left(2x-5\right)\left(x+2\right)\left(x+1\right)}{\left(2x^2+2\right)\left(x^2-1\right)}\right]:\left[\frac{5\cdot2}{2\left(x+1\right)\left(x-1\right)}+\frac{3\left(x-1\right)}{2\left(x^2-1\right)}-\frac{3\left(x+1\right)}{2\left(x^2-1\right)}\right]\)

\(A=\left[\frac{3\left(x+2\right)\left(x-1\right)+\left(2x-5\right)\left(x+2\right)\left(x+1\right)}{\left(2x^2+2\right)\left(x^2-1\right)}\right]:\left[\frac{10}{2\left(x^2-1\right)}+\frac{3x-3}{2\left(x^2-1\right)}-\frac{3x+3}{2\left(x^2-1\right)}\right]\)

\(A=\left[\frac{\left(x+2\right)\left[3x-3+\left(2x-5\right)\left(x+1\right)\right]}{\left(2x^2+2\right)\left(x^2-1\right)}\right]:\left[\frac{10+3x-3-3x-3}{2\left(x^2-1\right)}\right]\)

\(A=\left[\frac{\left(x+2\right)\left(3x-3+2x^2+2x-5x-5\right)}{\left(2x^2+2\right)\left(x^2-1\right)}\right]:\frac{4}{2\left(x^2-1\right)}\)

\(A=\frac{\left(x+2\right)\left(2x^2-8\right)}{\left(2x^2+2\right)\left(x^2-1\right)}\cdot\frac{\left(x^2-1\right)}{2}\)

\(A=\frac{\left(x+2\right)2\left(x^2-4\right)}{2\left(2x^2+2\right)}\)

\(A=\frac{2\left(x+2\right)\left(x-2\right)\left(x+2\right)}{4\left(x^2+1\right)}\)

\(A=\frac{\left(x+2\right)^2\left(x-2\right)}{2\left(x^2+1\right)}\)

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