d: \(5\left(x^2-1\right)\left(x^2+1\right)-2x\left(x-1\right)=2x-1-3\left(4x^2-3\right)\)
=>\(5\left(x^4-1\right)-2x^2+2x=2x-1-12x^2+9\)
=>\(5x^4-5-2x^2+2x=-12x^2+2x+8\)
=>\(5x^4-2x^2+2x-5+12x^2-2x-8=0\)
=>\(5x^4+10x^2-13=0\)
=>\(x^4+2x^2-\frac{13}{5}=0\)
=>\(x^4+2x^2+1-\frac{18}{5}=0\)
=>\(\left(x^2+1\right)^2=\frac{18}{5}\)
=>\(x^2+1=\frac{3\sqrt2}{\sqrt5}=\frac{3\sqrt{10}}{5}\)
=>\(x^2=\frac{3\sqrt{10}-5}{5}=\frac{15\sqrt{10}-25}{25}\)
=>\(x=\pm\frac{\sqrt{15\sqrt{10}-25}}{5}\)
c: \(x^2\left(x^2+2\right)-x^3\left(6x-1\right)=x^2\left(x-9\right)+2\left(x^2+2\right)\)
=>\(x^4+2x^2-6x^4+x^3=x^3-9x^2+2x^2+4\)
=>\(-5x^4+x^3=x^3-7x^2+4\)
=>\(-5x^4+7x^2-4=0\)
=>\(5x^4-7x^2+4=0\)
=>\(x^4-\frac75x^2+\frac45=0\)
=>\(x^4-2\cdot x^2\cdot\frac{7}{10}+\frac{49}{100}+\frac{31}{100}=0\)
=>\(\left(x^2-\frac{7}{10}\right)^2+\frac{31}{100}=0\) (vô lý)
=>x∈∅
