\(\left(x+3\right)^2\left(x^2+6x+1\right)=9\)

\(\Leftrightarrow\left(x+3\right)^2\left(x^2+6x+9-8\right)=9\)

\(\Leftrightarrow\left(x+3\right)^2\left[\left(x+3\right)^2-8\right]=9\)

\(\Leftrightarrow\left(x+3\right)^4-8\left(x+3\right)^2-9=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(x+3\right)^2=-1\left(loai\right)\\\left(x+3\right)^2=9\left(tm\right)\end{matrix}\right.\)

\(\left(x+3\right)^2=9\Leftrightarrow\left[{}\begin{matrix}x+3=3\\x+3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-6\end{matrix}\right.\) vậy........

2. \(x\left(x+2\right)\left(x+3\right)\left(x+5\right)=280\)

\(\Leftrightarrow x\left(x+5\right)\left(x+2\right)\left(x+3\right)=280\)

\(\Leftrightarrow\left(x^2+5x\right)\left(x^2+5x+6\right)=280\)

Đặt \(x^2+5x+3=t\)

\(\Rightarrow\left(t-3\right)\left(t+3\right)=280\)

\(\Leftrightarrow t^2-9=280\)

\(\Leftrightarrow t^2=289\Leftrightarrow\left[{}\begin{matrix}t=17\\t=-17\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2+5x+3=17\\x^2+5x+3=-17\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2+5x-14=0\\x^2+5x+20=0\end{matrix}\right.\)

\(\Leftrightarrow x^2+5x-14=0\text{(vì }x^2+5x+20=\left(x+\dfrac{5}{2}\right)^2+\dfrac{55}{4}>0\forall x\text{)}\)

\(\Leftrightarrow x^2-2x+7x-14=0\)

\(\Leftrightarrow x\left(x-2\right)+7\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+7\right)=0\)

\(\Leftrightarrow\) x - 2 = 0 hoặc x + 7 = 0

\(\Leftrightarrow\) x = 2 hoặc x = - 7

Vậy x = 2 hoặc x = -7.

3. \(\left(x+3\right)\left(x+4\right)\left(x+5\right)=x\)

\(\Leftrightarrow\left(x+3\right)\left(x+4\right)\left(x+5\right)-x=0\)

\(\Leftrightarrow x^3+12x^2+47x+60-x=0\)

\(\Leftrightarrow x^3+12x^2+46x+60=0\)

\(\Leftrightarrow x^3+6x^2+6x^2+36x+10x+60=0\)

\(\Leftrightarrow x^2\left(x+6\right)+6x\left(x+6\right)+10\left(x+6\right)=0\)

\(\Leftrightarrow\left(x+6\right)\left(x^2+6x+10\right)=0\)

\(\Leftrightarrow x+6=0\text{(vì }x^2+6x+10=\left(x+3\right)^2+1>0\forall x\text{)}\)

\(\Leftrightarrow x=-6\)

Vậy x = -6.

4.\(\dfrac{1}{x\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+6\right)}=\dfrac{1}{9}\)

\(\Leftrightarrow2\left[\dfrac{1}{x\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+6\right)}\right]=\dfrac{2}{9}\)

\(\Leftrightarrow\dfrac{2}{x\left(x+2\right)}+\dfrac{2}{\left(x+2\right)\left(x+4\right)}+\dfrac{2}{\left(x+4\right)\left(x+6\right)}=\dfrac{2}{9}\)

\(\Leftrightarrow\dfrac{1}{x}-\dfrac{1}{x+2}+\dfrac{1}{x+2}-\dfrac{1}{x+4}+\dfrac{1}{x+4}-\dfrac{1}{x+6}=\dfrac{2}{9}\)

\(\Leftrightarrow\dfrac{1}{x}-\dfrac{1}{x+6}=\dfrac{2}{9}\)

\(\Leftrightarrow\dfrac{6}{x\left(x+6\right)}=\dfrac{2}{9}\)

\(\Leftrightarrow2x\left(x+6\right)=54\)

\(\Leftrightarrow2x^2+12x-54=0\)

\(\Leftrightarrow2x^2-6x+18x-54=0\)

\(\Leftrightarrow2x\left(x-3\right)+18\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(2x+18\right)=0\)

\(\Leftrightarrow2\left(x-3\right)\left(x+9\right)=0\)

\(\Leftrightarrow\) x - 3 = 0 hoặc x + 9 = 0

\(\Leftrightarrow\) x = 3 hoặc x = -9

Vậy x = 3 hoặc x = -9.

\(\left(x^2-6x+9\right)+15\left(x^2-6x+10\right)=1\)

\(\Leftrightarrow\left(x-3\right)^2+15\left[\left(x-3\right)^2+1\right]=1\)

\(\Leftrightarrow16\left(x-3\right)^2+15=1\)

\(\Leftrightarrow16\left(x-3\right)^2=-14\)

=> Phương trình vô nghiệm 

\(\left(x^2-6x+9\right)-15\left(x^2-6x+10\right)=1\)

Đặt : \(x^2-6x+9=\left(x-3\right)^2=t\) thay vào pt ta được :

\(t^2-15\left(t+1\right)=1\)

\(\Leftrightarrow t^2-15t-16=0\)

\(\Leftrightarrow\left(t+1\right)\left(t-16\right)=0\)

\(\Leftrightarrow t=\left\{{}\begin{matrix}16\\-1\end{matrix}\right.\)

với : \(t=-1\) thì \(\left(x-3\right)^2=-1\)

\(\Rightarrow ptvonghiem\)

Với : \(t=16\) thì \(\left(x-3\right)^2=16\)

\(\Leftrightarrow x\in\left\{{}\begin{matrix}7\\-1\end{matrix}\right.\)

\(vay...\)

thôi chết rồi em nhầm đáng lẽ là : \(\left(x^2-6x+9\right)^2\) á

\(\sqrt{3x^2-6x-6}=3\sqrt{\left(2-x\right)^5}+\left(7x-19\right)\sqrt{2-x}\)

Điều kiện: \(\hept{\begin{cases}3x^2-6x-6\ge0\\2-x\ge0\end{cases}}\)

\(\Rightarrow x\le1-\sqrt{3}\)

Ta có:

\(\frac{\sqrt{3x^2-6x-6}}{\sqrt{2-x}}=3\left(2-x\right)^2+\left(7x-19\right)\) (điều kiện \(x\le\frac{5}{6}-\frac{\sqrt{109}}{6}\))

\(\Leftrightarrow\frac{3x^2-6x-6}{2-x}=9x^4-30x^3-17x^2+70x+49\)

\(\Leftrightarrow\left(x+1\right)\left(3x-8\right)\left(3x^3-11x^2+4+13\right)=0\)

(Kết hợp với điều kiện ta suy ra) 

\(\Leftrightarrow x=-1\)

x = 1 nha bạn

Cách giải y hệt bạn alibaba nguyễn. Các bạn làm theo nha

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a, ĐK: \(x\ge1\)

Đặt \(\sqrt{5x-1}=a;\sqrt{x-1}=b\left(a,b\ge0\right)\)

\(pt\Leftrightarrow\left(a+b\right)\left(\dfrac{a^2+b^2}{2}-ab\right)=a^2-b^2\)

\(\Leftrightarrow\left(a+b\right)\left(a-b\right)^2=2\left(a-b\right)\left(a+b\right)\)

\(\Leftrightarrow\left(a+b\right)\left(a-b\right)\left(a-b-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a=b\\a=b+2\end{matrix}\right.\)

TH1: \(a=b\Leftrightarrow\sqrt{5x-1}=\sqrt{x-1}\Leftrightarrow x=0\left(l\right)\)

TH2: \(a=b+2\Leftrightarrow\sqrt{5x-1}=\sqrt{x-1}+2\)

\(\Leftrightarrow5x-1=x-1+4+4\sqrt{x-1}\)

\(\Leftrightarrow4x-4-4\sqrt{x-1}=0\)

\(\Leftrightarrow4x-4-4\sqrt{x-1}+1=1\)

\(\Leftrightarrow\left(2\sqrt{x-1}-1\right)^2=1\)

\(\Leftrightarrow\left[{}\begin{matrix}2\sqrt{x-1}-1=1\\2\sqrt{x-1}-1=-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-1}=1\\\sqrt{x-1}=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=1\end{matrix}\right.\)

a/

\(\Leftrightarrow\left[{}\begin{matrix}x^2-5x-4=x^2-4\\x^2-5x-4=4-x^2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}-5x=0\\2x^2-5x-8=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\frac{5\pm\sqrt{89}}{4}\\\end{matrix}\right.\)

b/ - Với \(x\ge3\) pt trở thành:

\(x-1+3\left(x-3\right)=6\Leftrightarrow4x=16\Rightarrow x=4\)

- Với \(x\le1\) pt trở thành:

\(1-x+3\left(3-x\right)=6\)

\(\Leftrightarrow x=1\)

- Với \(1< x< 3\) pt trở thành:

\(x-1+3\left(3-x\right)=6\)

\(\Leftrightarrow-2x=-2\Rightarrow x=1\) (loại)

c/ ĐKXĐ: \(x\ne\pm2\)

\(\left[{}\begin{matrix}\frac{x^2-6x-4}{x^2-4}=1\\\frac{x^2-6x-4}{x^2-4}=-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2-6x-4=x^2-4\\x^2-6x-4=4-x^2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}-6x=0\\2x^2-6x-8=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-1\\x=4\end{matrix}\right.\)

d/ - Với \(x\ge2\) pt trở thành:

\(x-1-2\left(x-2\right)=x^2-x-3\)

\(\Leftrightarrow x^2=6\Rightarrow\left[{}\begin{matrix}x=\sqrt{6}\\x=-\sqrt{6}\left(l\right)\end{matrix}\right.\)

- Với \(x\le1\) pt trở thành:

\(1-x-2\left(2-x\right)=x^2-x-3\) làm tương tự

- Với \(1< x< 2\):

\(x-1-2\left(2-x\right)=x^2-x-3\)