Cho f(x) = ax^3 + 4x(x^2 - x) - 4x + 8; g(x) = x^3 - 4x(bx + 1) + c - 3 Trong đó a, b, c
Cho f(x) = ax3 + 4x(x2 – x) – 4x + 8; g(x) = x3 – 4x(bx + 1) + c – 3
Trong đó a, b, c là hằng số. Xác định a, b, c để f(x) = g(x).
Ta có: f(x) = ax3 + 4x(x2 – x) – 4x + 8
= (a + 4)x3 − 4x2 – 4x + 8
g(x) = x3 – 4x(bx + 1) + c – 3
= x3 – 4bx2 – 4x + c – 3
Để f(x) = g(x) thì:
\(\left\{ \begin{array}{l}a + 4 = 1\\ - 4 = - 4b\\8 = c - 3\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}a = - 3\\b = 1\\c = 11\end{array} \right.\)
Vậy a = −3; b = 1; c = 11.