a/
\(\left(x^2+2x\right)\left(x^2+2x+2\right)+1=0\)
\(\Leftrightarrow\left(x^2+2x\right)^2+2\left(x^2+2x\right)+1=0\)
\(\Leftrightarrow\left(x^2+2x+1\right)^2=0\)
\(\Leftrightarrow x+1=0\)
\(\Rightarrow x=1\)
b/
\(y^2+2y+1+\left(2^x\right)^2-2.2^x+1=0\)
\(\Leftrightarrow\left(y+1\right)^2+\left(2^x-1\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}y+1=0\\2^x-1=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}y=-1\\x=0\end{matrix}\right.\)
c/
ĐKXĐ: \(x\ne\left\{-2;-4;-6;-8\right\}\)
\(\frac{\left(x+2\right)^2+2}{x+2}+\frac{\left(x+8\right)^2+8}{x+8}=\frac{\left(x+4\right)^2+4}{x+4}+\frac{\left(x+6\right)^2+6}{x+6}\)
\(\Leftrightarrow x+2+\frac{2}{x+2}+x+8+\frac{8}{x+8}=x+4+\frac{4}{x+4}+x+6+\frac{6}{x+6}\)
\(\Leftrightarrow\frac{1}{x+2}+\frac{4}{x+8}=\frac{2}{x+4}+\frac{3}{x+6}\)
\(\Leftrightarrow\frac{1}{x+2}-\frac{2}{x+4}+\frac{4}{x+8}-\frac{3}{x+6}=0\)
\(\Leftrightarrow\frac{-x}{\left(x+2\right)\left(x+4\right)}+\frac{x}{\left(x+8\right)\left(x+6\right)}=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\frac{1}{\left(x+2\right)\left(x+4\right)}=\frac{1}{\left(x+6\right)\left(x+8\right)}\left(1\right)\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow\left(x+2\right)\left(x+4\right)=\left(x+6\right)\left(x+8\right)\)
\(\Leftrightarrow8x=-40\Rightarrow x=-5\)