Ta có:
(x2 - 3x + 2)(x2 + 15x + 56) + 8 = 0
\(\Leftrightarrow\) [(x - 2)(x - 1)][(x + 7)(x + 8)] + 8 = 0
\(\Leftrightarrow\) [(x - 2)(x + 8)][(x - 1)(x + 7)] + 8 = 0
\(\Leftrightarrow\) (x2 + 6x - 16)(x2 + 6x - 7) + 8 = 0 (*)
Đặt x2 + 6x - 16 = a \(\Leftrightarrow\) a = (x + 3)2 - 25 \(\ge\) -25
Phương trình (*) trở thành:
a(a + 9) + 8 = 0
\(\Leftrightarrow\) 4a2 + 36a + 32 = 0
\(\Leftrightarrow\) (2a + 9)2 = 49
\(\Leftrightarrow\) \(\left[{}\begin{matrix}a=-1\left(TMĐK\right)\\a=-8\left(TMĐK\right)\end{matrix}\right.\)
+) Nếu a = -1 thì (x + 3)2 - 25 = -1
\(\Leftrightarrow\) x = \(\pm\sqrt{24}-3\)
+) Nếu a = -8 thì (x + 3)2 - 25 = -8
\(\Leftrightarrow\) x = \(\pm\sqrt{17}-3\)
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