Đáp án:
x=0
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ne \left\{ {3;4;5;6} \right\}\\
Pt \to x\left( {x - 5} \right)\left( {x - 4} \right)\left( {x - 6} \right) + x\left( {x - 3} \right)\left( {x - 4} \right)\left( {x - 6} \right)\\
= x\left( {x - 3} \right)\left( {x - 5} \right)\left( {x - 6} \right) + x\left( {x - 3} \right)\left( {x - 5} \right)\left( {x - 4} \right)\\
\to \left( {{x^2} - 5x} \right)\left( {{x^2} - 10x + 24} \right) + \left( {{x^2} - 3x} \right)\left( {{x^2} - 10x + 24} \right)\\
= \left( {{x^2} - 6x} \right)\left( {{x^2} - 8x + 15} \right) + \left( {{x^2} - 4x} \right)\left( {{x^2} - 8x + 15} \right)\\
\to {x^4} - 15{x^3} + 74{x^2} - 120x + {x^4} - 13{x^3} + 54{x^2} - 72x\\
= {x^4} - 14{x^3} + 63{x^2} - 90x + {x^4} - 12{x^3} + 47{x^2} - 60x\\
\to - 2{x^3} + 18{x^2} - 42x = 0\\
\to x = 0\left( {TM} \right)
\end{array}\)
