\(a,ĐK:x\le2\\ PT\Leftrightarrow x^2-x-8=4-2x\Leftrightarrow x^2+x-12=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\left(ktm\right)\\x=-4\left(tm\right)\end{matrix}\right.\Leftrightarrow x=-4\\ b,ĐK:5x^2+10x+1\ge0\\ PT\Leftrightarrow5x^2+10x+1=\left(7-x^2-2x\right)^2\\ \Leftrightarrow5x^2+10x+1=x^4+4x^2+49-14x^2+4x^3-28x\\ \Leftrightarrow x^4+4x^3-15x^2-38x+48=0\\ \Leftrightarrow x^4-x^3+5x^3-5x^2-10x^2+10x-48x+48=0\\ \Leftrightarrow\left(x-1\right)\left(x^3+5x^2-10x-48\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x^3+3x^2+2x^2+6x-16x-48\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+3\right)\left(x^2+2x-16\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-3\\x^2+2x-16=0\left(1\right)\end{matrix}\right.\)
\(\Delta\left(1\right)=4+64=68\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-2-2\sqrt{17}}{2}=-1-\sqrt{17}\\x=\dfrac{-2+2\sqrt{17}}{2}=-1+\sqrt{17}\end{matrix}\right.\)
Vậy pt có nghiệm ...
