Question

Giải phương trình:

(x + 1)³ - (x - 2)³ = (3x - 1)(3x + 1)

Answer 1

(x + 1)³ - (x - 2)³ = (3x - 1)(3x + 1)

\(\Leftrightarrow\) (x + 1 - x + 2)[(x + 1)² + (x + 1)(x - 2) + (x - 2)²] = (3x - 1)(3x + 1)

\(\Leftrightarrow\) 3(x² + 2x + 1 + x² - 2x + x - 2 + x² - 4x + 4) = 9x² - 1

\(\Leftrightarrow\) 3(3x² - 3x + 3) = 9x² - 1

\(\Leftrightarrow\) 9x² - 9x + 9 = 9x² - 1

\(\Leftrightarrow\) 9x² - 9x² - 9x = -1 - 9

\(\Leftrightarrow\) -9x = -10

\(\Leftrightarrow\) x = \(\frac{10}{9}\)

Vậy S = {\(\frac{10}{9}\)}

Chúc bn học tốt!!