Question

Tìm x : x³ - 6x² + 2x + 3 = 0

Giúp mình với

Answer 1

\(x^3-6x^2+2x+3=0\)

\(\Leftrightarrow x^3-5x^2-3x-x^2+5x+3=0\)

\(\Leftrightarrow x\left(x^2-5x-3\right)-\left(x^2-5x-3\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^2-5x-3\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x-1=0\\x^2-5x-3=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=1\\\Delta_{x^2-5x-3}=\left(-5\right)^2-\left[-4\left(1.3\right)\right]=37\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=1\\x_{1,2}=\frac{5\pm\sqrt{37}}{2}\end{array}\right.\)