(x^2+x)^2 + 4(x^2+x)=4

=>(x^2+x)^2 + 4(x^2+x)+4-8=0

=>(x^2+x+2)^2-8 = 0

Chịu rồi!

mk chỉnh lại đề nhé:  

     \(\left(\frac{x+1}{x-2}\right)^2+\frac{x+1}{x-4}-3\left(\frac{2x-4}{x-4}\right)^2=0\)

\(\Leftrightarrow\) \(\left(\frac{x+1}{x-2}\right)^2+\frac{x+1}{x-4}-12\left(\frac{x-2}{x-4}\right)^2=0\)

Đặt:    \(\frac{x+1}{x-2}=a;\)   \(\frac{x-2}{x-4}=b\)

\(\Rightarrow\)\(a.b=\frac{x+1}{x-2}.\frac{x-2}{x-4}=\frac{x+1}{x-4}\)

Khi đó phương trình trở thành:

   \(a^2-ab-12b^2=0\)

\(\Leftrightarrow\)\(\left(a-3b\right)\left(a+4b\right)=0\)

đến đây bn thay trở lại rồi tìm nghiệm

+)  \(a=3b\) thì  phương trình vô nghiệm

+)  \(a=-4b\)thì phương trình có tập nghiệm     \(S=\left\{3;\frac{4}{5}\right\}\)

P/S: bn tham khảo nhé

bạn chắt mình giải đúng chứ

\(x^2\left(x^2-4\right)=3\left(x^2-4\right)\)

\(\Rightarrow x^2\left(x^2-4\right)-3\left(x^2-4\right)=0\)

\(\Rightarrow\left(x^2-4\right)\left(x^2-3\right)=0\)

\(\Rightarrow\left[\begin{array}{nghiempt}x^2-4=0\\x^2-3=0\end{array}\right.\)

\(\Rightarrow\left[\begin{array}{nghiempt}\left[\begin{array}{nghiempt}x=2\\x=-2\end{array}\right.\\\left[\begin{array}{nghiempt}x=\sqrt{3}\\x=-\sqrt{3}\end{array}\right.\end{array}\right.\)

Vậy x=2; x= - 2 ; x=\(\sqrt{3}\) ; x=\(-\sqrt{3}\)

Có : \(x^2\left(x^2-4\right)=3\left(x^2-4\right)\)

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

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

\(\Leftrightarrow\left[\begin{array}{nghiempt}x^2-4=0\\x^2-3=0\end{array}\right.\) \(\Leftrightarrow\left[\begin{array}{nghiempt}x^2=4\\x^2=3\end{array}\right.\) \(\Leftrightarrow\left[\begin{array}{nghiempt}x=2;x=-2\\x=\sqrt{3};x=-\sqrt{3}\end{array}\right.\)

Vậy \(x=-2;x=2;x=-\sqrt{3};x=\sqrt{3}\)

\(5^x-2-3^2=2^4-\left(2^8x2^4-2^{10}x2^2\right)\)

\(5^x-2-3^2=2^4-\left(2^{8+4}-2^{10+2}\right)\)

\(5^x-2-3^2=2^4-\left(2^{12}-2^{12}\right)\)

\(5^x-2-3^2=2^4-0\)

\(5^x-2-3^2=2^4\)

\(5^x-2-9=16\)

\(5^x-2=16+9\)

\(5^x-2=25\)

\(5^x=25+2\)

\(5^x=27\)

Bởi vì 27 không phân tích được 1 số có số mũ là 2

\(\Rightarrow\) Không tồn tại x

\(5^{x-2}-9=16-\left(256.16-1024.4\right)\)

\(\Rightarrow5^{x-2}-9=16-\left(4096-4096\right)\)

\(\Rightarrow5^{x-2}-9=16-0\)

\(\Rightarrow5^{x-2}-9=16\)

\(\Rightarrow5^{x-2}=25\)

\(\Rightarrow x-2=25:5\)

\(\Rightarrow x-2=3\)

\(\Rightarrow x=5\)

\(5^{x-2}-3^2=2^4-\left(2^8\cdot2^4-2^{10}\cdot2^2\right)\)

\(\Rightarrow5^{x-2}-3^2=2^4-\left(2^{12}-2^{12}\right)\)

\(\Rightarrow5^{x-2}-9=16-0\)

\(\Rightarrow5^{x-2}=16+9\)

\(\Rightarrow5^{x-2}=25\)

\(\Rightarrow5^{x-2}=5^2\)

\(\Rightarrow x-2=2\)

\(\Rightarrow x=2+2\)

\(\Rightarrow x=4\)

Vậy: x=4

\(\sqrt{4-x^2}=\sqrt{x+2}\) (ĐK: \(-2\le x\le2\))

\(\Leftrightarrow4-x^2=x+2\)

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

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

\(\Leftrightarrow\left(x-1\right)\left(x+2\right)=0\)

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

_______

\(\sqrt{9x^2-4}=2\sqrt{3x-2}\) (ĐK: \(x\ge\dfrac{2}{3}\)) 

\(\Leftrightarrow9x^2-4=4\left(3x-2\right)\)

\(\Leftrightarrow9x^2-4=12x-8\)

\(\Leftrightarrow9x^2-12x+4=0\)

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

\(\Leftrightarrow3x=2\)

\(\Leftrightarrow x=\dfrac{2}{3}\left(tm\right)\)

\(\frac{x-1}{x-2}+\frac{x+3}{x-4}=\frac{2}{\left(x-2\right)\left(x-4\right)}\)

\(ĐKXĐ:x\ne2,x\ne4\)

\(MC:\left(x-2\right)\left(x-4\right)\)

\(PT\Leftrightarrow\left(x-1\right)\left(x-4\right)+\left(x+3\right)\left(x-2\right)=2\)

\(\Leftrightarrow x^2-5x+4+x^2+x-6=2\)

\(\Leftrightarrow2x^2-4x-4=0\)

\(\Leftrightarrow2\left(x^2-2x-2\right)=0\)

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

\(\Leftrightarrow x\left(x-2\right)=2\)

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

Vậy giờ mình kết luận x=? hả bạn? Mình dở toán lắm. (T-T)