\(p=\left(x+1\right)\left(x^2-x+1\right)+x-\left(x-1\right)\left(x^2+x+1\right)+2010\)\(=\left(x^3+1\right)+x-\left(x^3-1\right)+2010=x^3+1+x-x^3+1+2010=x+2012\)Với \(x=-2010\Rightarrow p=-2010+2012=2\)

\(q=16x\left(4x^2-5\right)-\left(4x+1\right)\left(16x^2-4x+1\right)=64x^3-80x-64x^3-1=-80x-1\)Với \(x=\dfrac{1}{5}\Rightarrow q=-80.\dfrac{1}{5}-1=-17\)

\(\left(4x+1\right)\left(-4x+1\right)-16x\left(-5\right)=17\)

\(\Leftrightarrow\left(1+4x\right)\left(1-4x\right)+80x-17=0\)

\(\Leftrightarrow1-16x^2+80x-17=0\)

\(\Leftrightarrow-16x^2-16+80x=-16\left(x^2-5x+1\right)=0\Leftrightarrow-16\left[\left(x^2-5x+\dfrac{25}{4}\right)-\dfrac{21}{4}\right]=0\Leftrightarrow-16\left(x-\dfrac{5}{2}\right)^2+84=0\Rightarrow\left(x-\dfrac{5}{2}\right)^2=\dfrac{21}{4}\) \(\Rightarrow\left[{}\begin{matrix}x-\dfrac{5}{2}=\sqrt{\dfrac{21}{4}}\\x-\dfrac{5}{2}=-\sqrt{\dfrac{21}{4}}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{21}{4}}+\dfrac{5}{2}\\x=-\sqrt{\dfrac{21}{4}}+\dfrac{5}{2}\end{matrix}\right.\)