Đáp án:
x∈{1;2;3}
Giải thích các bước giải:
\(
\begin{array}{l}
x^4 - 5x^3 + x^2 + 21x - 18 = 0 \\
\Leftrightarrow x^4 - x^3 - 4x^3 + 4x^2 - 3x^2 + 3x + 18x - 18 = 0 \\
\Leftrightarrow x^3 (x - 1) - 4x^2 (x - 1) - 3x(x - 1) + 18(x - 1) = 0 \\
\Leftrightarrow (x - 1)(x^3 - 4x^2 - 3x + 18) = 0 \\
\Leftrightarrow (x - 1)(x^3 + 2x^2 - 6x^2 - 12x + 9x + 18) = 0 \\
\Leftrightarrow (x - 1){\rm{[x}}^{\rm{2}} (x + 2) - 6x(x + 2) + 9(x + 2){\rm{] = 0}} \\
\Leftrightarrow (x - 1)(x - 2)(x^2 - 6x + 9) = 0 \\
\Leftrightarrow (x - 1)(x - 2)(x - 3)^2 = 0 \\
\Leftrightarrow \left[ {\begin{array}{*{20}c}
{x - 1 = 0} \\
{x - 2 = 0} \\
{x - 3 = 0} \\
\end{array}} \right. \Leftrightarrow \left[ {\begin{array}{*{20}c}
{x = 1} \\
{x = 2} \\
{x = 3} \\
\end{array}} \right. \\
\end{array}
\)
