Tìm x biết: x^4 + 2x^3 – 6x – 9 = 0.
Tìm x biết: x4 + 2x3 – 6x – 9 = 0.
Lời giải
Ta có x4 + 2x3 – 6x – 9 = 0.
⇔ (x4 + 2x3 + x2) – (x2 + 6x + 9) = 0.
⇔ (x2 + x)2 – (x + 3)2 = 0.
⇔ (x2 + x – x – 3)(x2 + x + x + 3) = 0.
⇔ (x2 – 3)(x2 + 2x + 3) = 0.
\( \Leftrightarrow \left[ \begin{array}{l}{x^2} - 3 = 0\\{x^2} + 2x + 3 = 0\,\,\left( {vo\,\,nghiem} \right)\end{array} \right.\)
\( \Leftrightarrow x = \pm \sqrt 3 \).
Vậy \(x = \pm \sqrt 3 \).