Question

giải phương trình sau

(x^2+7x)^2 - 2(x^2+7x)-24=0

Answer 1

(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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