a)
$\,\,\,\,\,\,\,3{{\left( {{x}^{2}}-x+1 \right)}^{2}}-2{{\left( x+1 \right)}^{2}}=5\left( {{x}^{3}}+1 \right)$
$\Leftrightarrow 3\left( {{x}^{4}}+{{x}^{2}}+1-2{{x}^{3}}+2{{x}^{2}}-2x \right)-2\left( {{x}^{2}}+2x+1 \right)-5\left( {{x}^{3}}+1 \right)=0$
$\Leftrightarrow 3{{x}^{4}}-11{{x}^{3}}+7{{x}^{2}}-10x-4=0$
$\Leftrightarrow \left( 3{{x}^{4}}-2{{x}^{3}}+4{{x}^{2}} \right)+\left( -9{{x}^{3}}+6{{x}^{2}}-12x \right)+\left( -3{{x}^{2}}+2x-4 \right)=0$
$\Leftrightarrow {{x}^{2}}\left( 3{{x}^{2}}-2x+4 \right)-3x\left( 3{{x}^{2}}-2x+4 \right)-\left( 3{{x}^{2}}-2x+4 \right)=0$
$\Leftrightarrow \left( 3{{x}^{2}}-2x+4 \right)\left( {{x}^{2}}-3x-1 \right)=0$
$\Leftrightarrow\left[\begin{array}{1}3x^2-2x+4=0\,\,\,\,\,\left(1\right)\\x^2-3x-1=0\,\,\,\,\,\left(2\right)\end{array}\right.$
$\left( 1 \right)\Leftrightarrow {{\Delta }_{1}}=-44\,\,<\,\,0$
$\to $ phương trình $\left( 1 \right)$ vô nghiệm
$\left( 2 \right)\Leftrightarrow {{\Delta }_{2}}=13\,\,\,\,\,\to \,\,\,\,\,\sqrt{{{\Delta }_{2}}}=\sqrt{13}$
$\to\left[\begin{array}{1}x_1=\dfrac{3+\sqrt{13}}{2}\\x_2=\dfrac{3-\sqrt{13}}{2}\end{array}\right.$
b)
$\,\,\,\,\,\,\,2{{\left( {{x}^{2}}+x+1 \right)}^{2}}-7{{\left( x-1 \right)}^{2}}=13\left( {{x}^{3}}-1 \right)$
$\Leftrightarrow 2\left( {{x}^{4}}+{{x}^{2}}+1+2{{x}^{3}}+2{{x}^{2}}+2x \right)-7\left( {{x}^{2}}-2x+1 \right)-13\left( {{x}^{3}}-1 \right)=0$
$\Leftrightarrow 2{{x}^{4}}-9{{x}^{3}}-{{x}^{2}}+18x+8=0$
$\Leftrightarrow \left( 2{{x}^{4}}-12{{x}^{3}}+16{{x}^{2}} \right)+\left( 3{{x}^{3}}-18{{x}^{2}}+24x \right)+\left( {{x}^{2}}-6x+8 \right)=0$
$\Leftrightarrow 2{{x}^{2}}\left( {{x}^{2}}-6x+8 \right)+3x\left( {{x}^{2}}-6x+8 \right)+\left( {{x}^{2}}-6x+8 \right)=0$
$\Leftrightarrow \left( {{x}^{2}}-6x+8 \right)\left( 2{{x}^{2}}+3x+1 \right)=0$
$\Leftrightarrow\left[\begin{array}{1}x^2-6x+8=0\,\,\,\,\,\left(1\right)\\2x^3+3x+1=0\,\,\,\,\,\left(2\right)\end{array}\right.$
$\left( 1 \right)\Leftrightarrow {{\Delta }_{1}}=4\,\,\,\,\,\to \,\,\,\,\,\sqrt{{{\Delta }_{1}}}=2$
$\to\left[\begin{array}{1}x_1=4\\x_2=2\end{array}\right.$
$\left( 2 \right)\Leftrightarrow {{\Delta }_{2}}=1\,\,\,\,\,\to \,\,\,\,\,\sqrt{{{\Delta }_{2}}}=1$
$\to\left[\begin{array}{1}x_3=-\dfrac{1}{2}\\x_4=-1\end{array}\right.$
