1. x2 + 7x + 2 = 0
\(\Leftrightarrow\) (x + \(\frac{7}{2}\))2 - \(\frac{41}{4}\) = 0
\(\Leftrightarrow\) (x + \(\frac{7}{2}\) - \(\sqrt{\frac{41}{4}}\))(x + \(\frac{7}{2}\) + \(\sqrt{\frac{41}{4}}\)) = 0
\(\Leftrightarrow\) x + \(\frac{7}{2}\) - \(\sqrt{\frac{41}{4}}\) = 0 hoặc x + \(\frac{7}{2}\) + \(\sqrt{\frac{41}{4}}\) = 0
\(\Leftrightarrow\) x + \(\frac{7-\sqrt{41}}{2}\) = 0 hoặc x + \(\frac{7+\sqrt{41}}{2}\) = 0
\(\Leftrightarrow\) x = \(\frac{-7+\sqrt{41}}{2}\) và x = \(\frac{-7-\sqrt{41}}{2}\)
Vậy S = {\(\frac{-7+\sqrt{41}}{2}\); \(\frac{-7-\sqrt{41}}{2}\)}
2. x2 - x - 12 = 0
\(\Leftrightarrow\) (x - \(\frac{1}{2}\))2 - \(\frac{49}{4}\) = 0
\(\Leftrightarrow\) (x - \(\frac{1}{2}\) - \(\frac{7}{2}\))(x - \(\frac{1}{2}\) + \(\frac{7}{2}\)) = 0
\(\Leftrightarrow\) (x - 4)(x + 3) = 0
\(\Leftrightarrow\) x - 4 = 0 hoặc x + 3 = 0
\(\Leftrightarrow\) x = 4 và x = -3
Vậy S = {4; -3}
3. (x + 1)3 - (x - 2)3 = (3x - 1)(3x + 1)
\(\Leftrightarrow\) 9x2 - 9x + 9 = 9x2 - 1
\(\Leftrightarrow\) 9x2 - 9x + 9 - 9x2 + 1 = 0
\(\Leftrightarrow\) -9x + 10 = 0
\(\Leftrightarrow\) x = \(\frac{10}{9}\)
Vậy S = {\(\frac{10}{9}\)}
Chúc bn học tốt!!
