Đáp án+Giải thích các bước giải:
\(1.\quad(x^2-1)(x^2 +5x +6)=0\\\Leftrightarrow\left[ \begin{array}{l}x^2-1=0\\x^2 +5x +6=0\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x^2 =1\\(x+3)(x+2)=0\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=\pm1\\\left[ \begin{array}{l}x=-3\\x=-2\end{array} \right.\end{array} \right.\\2.\quad (x^2 -6x)^2 -2(x-3)^2 =0\\\Leftrightarrow x^4 -12x^3 +36x^2 -2(x^2 -6x +9)=81\\\Leftrightarrow x^4 -12x^3 +36x^2 -2x^2 +12x -18 =81\\\Leftrightarrow x^4 -3x^3 -9x^3 +34^2 +12x -99=0\\\Leftrightarrow x^4 -3x^3 -9x^3 +27x^2 +7x^2 -2x +33x -99=0\\\Leftrightarrow x^3(x-3)-9x^2(x-3)+7x(x-3) +33(x-3)=0\\\Leftrightarrow (x-3)(x^3 -9x^2 +7x +33)=0\\\Leftrightarrow (x-3)(x^3 -3x^2 -6x^2 +18x -11x +33)=0\\\Leftrightarrow (x-3)[x^2(x-3)-6x(x-3)-11(x-3)]=0\\\Leftrightarrow (x-3)^2(x^2 -6x -11)=0\\\Leftrightarrow \left[ \begin{array}{l}(x-3)^2=0\\x^2 -6x -11=0\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x-3=0\\x=\dfrac{-(-6)\pm\sqrt{(-6)^2 -4\times 1\times (-11)}}{2\times 1} \end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=3\\\left[ \begin{array}{l}x=\dfrac{6+4\sqrt{5}}{2}\\x=\dfrac{6-4\sqrt{5}}{2}\end{array} \right.\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=3\\\left[ \begin{array}{l}x=\dfrac{2(3+2\sqrt{5})}{2}\\x=\dfrac{2(3-2\sqrt{5})}{2}\end{array} \right.\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=3\\x=3+2\sqrt{5}\\x=3-2\sqrt{5}\end{array} \right.\\3.\quad x(x+1)(x+2)(x+3)=120\\\Leftrightarrow (x^2+x)(x+2)(x+3)=120\\\Leftrightarrow (x^3 +3x^2 +2x)(x+3)=120\\\Leftrightarrow x^4 +6x^3+11x +6x =120\\\Leftrightarrow x^4 -2x^3 +8x^3 -16x^2 +27x^2 -54x +60x -120=0\\\Leftrightarrow x^3(x-2)+8x^2(x-2) +27x(x-2)+60(x-2)=0\\\Leftrightarrow (x-2)(x^3 +8x^2 +27x +60)=0\\\Leftrightarrow (x-2)(x^3 +5x^2 +3x^2 +15x +12x +60)=0\\\Leftrightarrow (x-2)[x^2(x+5)+3x(x+5)+12(x+5)]=0\\\Leftrightarrow (x-2)(x+5)(x^2 +3x+12)=0\\\Leftrightarrow \left[ \begin{array}{l}x-2=0\\x+5=0\\x^2 +3x +12=0\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=2\\x=-5\\x=\dfrac{-3\pm\sqrt{3^2 -4\times 1\times 12}}{2\times 1}\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=2\\x=-5\\x=\dfrac{-3\pm\sqrt{-39}}{2}\quad (!) \Rightarrow x\notin \mathbb{R} \end{array} \right.\\4.\quad x^3 +5x^2 -10x -8=0\\\Leftrightarrow (x-2)(x^2 + 2x +4)+5x(x-2)=0\\\Leftrightarrow (x-2)(x^2 +2x+4+5x)=0\\\Leftrightarrow (x-2)(x^2 +7x +4)=0\\\Leftrightarrow \left[ \begin{array}{l}x-2=0\\x^2 +7x +4=0\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=2\\x=\dfrac{-7\pm\sqrt{7^2 -4\times 1\times 4}}{2\times 1}\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=2\\x=\dfrac{-7\pm\sqrt{33}}{2}\end{array} \right.\\\Leftrightarrow \left[ \begin{array}{l}x=2\\x=\dfrac{-7+\sqrt{33}}{2}\\x=\dfrac{-7-\sqrt{33}}{2}\end{array} \right.\)
