Đáp án:
Giải thích các bước giải:
ĐK: \(x \ne \{ 8;9;10;11\} \)
\(\begin{array}{l}
8\left( {x - 11} \right)\left( {x - 9} \right)\left( {x - 10} \right) + 11\left( {x - 8} \right)\left( {x - 9} \right)\left( {x - 10} \right) = 9\left( {x - 8} \right)\left( {x - 11} \right)\left( {x - 10} \right) + 10\left( {x - 8} \right)\left( {x - 11} \right)\left( {x - 9} \right)\\
\to \left( {8x - 88} \right)\left( {{x^2} - 19x + 90} \right) + \left( {11x - 88} \right)\left( {{x^2} - 19x + 90} \right) - \left( {9x - 72} \right)\left( {{x^2} - 21x + 110} \right) - \left( {10x - 80} \right)\left( {{x^2} - 20x + 99} \right) = 0\\
\to 8{x^3} - 240{x^2} + 2392x - 7920 + 11{x^3} - 297{x^2} + 2662x - 7920 - 9{x^3} + 261{x^2} - 2502x + 7920 - 10{x^3} + 280{x^2} - 2320x + 7920 = 0\\
\to 4{x^2} + 232x = 0\\
\to \left[ \begin{array}{l}
x = 0(TM)\\
x = - 58(TM)
\end{array} \right.
\end{array}\)
