(x2 + 7x)2 - 2(x2 + 7x) - 24 = 0
<=> (x2 + 7x)(x2 + 7x - 2) - 24 = 0 (1)
Đặt t = x2 + 7x - 1 = \(=\left(x+\frac{7}{2}\right)^2-\frac{53}{4}\)
(1) trở thành (t + 1)(t - 1) - 24 = 0
<=> t2 - 1 - 24 = 0
<=> t2 - 25 = 0
<=> t2 = 25
<=> t = 5 hoặc t = -5
+) t =\(\left(x+\frac{7}{2}\right)^2-\frac{53}{4}\) = 5
\(\Leftrightarrow\left(x+\frac{7}{2}\right)^2=\frac{73}{4}\)
\(\Leftrightarrow x=\frac{-7+\sqrt{73}}{2};x=\frac{-7-\sqrt{73}}{2}\)
+) t = \(\left(x+\frac{7}{2}\right)^2-\frac{53}{4}=-5\)
\(\Leftrightarrow\left(x+\frac{7}{2}\right)^2=\frac{33}{4}\)
\(\Leftrightarrow x=\frac{-7+\sqrt{33}}{2};x=\frac{-7-\sqrt{33}}{2}\)
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