Question

Cho f(x) = ax³ + bx² + cx +d. Biết f(0) = -5; f(1) = 9. f(2) = 31; f(3) = 88. Tìm a,b,c,d.

Answer 1

Lời giải:

\(\left\{\begin{matrix} f(0)=-5\\ f(1)=9\\ f(2)=31\\ f(3)=88\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} a.0^3+b.0^2+c.0+d=-5\\ a.1^3+b.1^2+c.1+d=9\\ a.2^3+b.2^2+c.2+d=31\\ a.3^3+b.3^2+c.3+d=88\end{matrix}\right.\)

\(\Leftrightarrow \left\{\begin{matrix} d=-5\\ a+b+c+d=9\\ 8a+4b+2c+d=31\\ 27a+9b+3c+d=88\end{matrix}\right.\) \(\Leftrightarrow \left\{\begin{matrix} d=-5\\ a+b+c=14(1)\\ 4a+2b+c=18(2)\\ 9a+3b+c=31(3)\end{matrix}\right.\)

Lấy \((2)-(1)\Rightarrow 3a+b=4(4)\)

Lấy $(3)-(2)\Rightarrow 5a+b=13(5)$

Lấy $(5)-(4)\Rightarrow a=4,5$

$\Rightarrow b=4-3a=-9,5$

$\Rightarrow c=14-a-b=19$

Vậy.........