Đáp án:
a) \(\left[ \begin{array}{l}
x = 0\\
x = - 4\\
x = 3\\
x = 7
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a)({x^2} + 5x + 6)({x^2} - 11x + 30) = 180\\
\to {x^4} - 11{x^3} + 30{x^2} + 5{x^3} - 55{x^2} + 150x + 6{x^2} - 66x + 180 = 180\\
\to {x^4} - 6{x^3} - 19{x^2} + 84x = 0\\
\to x\left( {{x^3} - 6{x^2} - 19x + 84} \right) = 0\\
\to \left[ \begin{array}{l}
x = 0\\
{x^3} + 4{x^2} - 10{x^2} - 40x + 21x + 84 = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 0\\
{x^2}\left( {x + 4} \right) - 10x\left( {x + 4} \right) + 21\left( {x + 4} \right) = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 0\\
\left( {x + 4} \right)\left( {{x^2} - 10x + 21} \right) = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 0\\
x = - 4\\
\left( {x - 3} \right)\left( {x - 7} \right) = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 0\\
x = - 4\\
x = 3\\
x = 7
\end{array} \right.\\
b)6{x^4} - 5{x^3} - 38{x^2} - 5x + 6 = 0\\
\to 6{x^4} - 2{x^3} - 3{x^3} + {x^2} - 39{x^2} + 13x - 18x + 6 = 0\\
\to 2{x^3}\left( {3x - 1} \right) - {x^2}\left( {3x - 1} \right) - 13x\left( {3x - 1} \right) - 18\left( {3x - 1} \right) = 0\\
\to \left( {3x - 1} \right)\left( {2{x^3} - {x^2} - 13x - 18} \right) = 0\\
\to \left[ \begin{array}{l}
x = \dfrac{1}{3}\\
2{x^3} - {x^2} - 13x - 18 = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{1}{3}\\
x = 3,298162145
\end{array} \right.
\end{array}\)
