(x + 3)(x + 4)(x + 5)(x + 6) + 1 = 0
\(\Leftrightarrow\) [(x + 3)(x + 6)][(x + 4)(x + 5)] + 1 = 0
\(\Leftrightarrow\) (x2 + 19x + 18)(x2 + 19x + 20) + 1 = 0
\(\Leftrightarrow\) (x2 + 19x + 19 - 1)(x2 + 19x + 19 + 1) + 1 = 0
\(\Leftrightarrow\) (x2 + 19x + 19)2 - 1 + 1 = 0
\(\Leftrightarrow\) (x2 + 19x + 19)2 = 0
\(\Leftrightarrow\) x2 + 19x + 19 = 0
\(\Leftrightarrow\) x2 + 2.\(\frac{19}{2}\).x + \(\frac{361}{4}\) + \(\frac{-285}{4}\) = 0
\(\Leftrightarrow\) (x + \(\frac{19}{2}\))2 - \(\frac{285}{4}\) = 0
\(\Leftrightarrow\) (x + \(\frac{19}{2}\) - \(\frac{\sqrt{285}}{2}\))(x + \(\frac{19}{2}\) + \(\frac{\sqrt{285}}{2}\)) = 0
\(\Leftrightarrow\left[{}\begin{matrix}x+\frac{19-\sqrt{285}}{2}=0\\x+\frac{19+\sqrt{285}}{2}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{\sqrt{285}-19}{2}\\x=\frac{-\sqrt{285}-19}{2}\end{matrix}\right.\)
Vậy S = {\(\frac{\sqrt{285}-19}{2}\); \(\frac{-\sqrt{285}-19}{2}\)}
Chúc bn học tốt!
\(\Leftrightarrow\left(x+3\right)\left(x+6\right)\left(x+4\right)\left(x+5\right)+1=0\)
\(\Leftrightarrow\left(x^2+9x+18\right)\left(x^2+9x+20\right)+1=0\)
\(\Leftrightarrow\left(x^2+9x+18\right)\left(x^2+9x+18+2\right)+1=0\)
\(\Leftrightarrow\left(x^2+9x+18\right)^2+2\left(x^2+9x+18\right)+1=0\)
\(\Leftrightarrow\left(x^2+9x+18+1\right)^2=0\)
\(\Leftrightarrow x^2+9x+19=0\) (bấm máy)
