Question

Tìm các đa thức A(x) và B(x) biết A(x) - B(x) = 4x - x^2 + 11 

và A(x) + 2B(x) = x^2 - x + 4

Answer 1

\(\left\{{}\begin{matrix}A\left(x\right)-B\left(x\right)=-x^2+4x+11\\A\left(x\right)+2B\left(x\right)=x^2-x+4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-3B\left(x\right)=-2x^2+5x+7\\A\left(x\right)-B\left(x\right)=-x^2+4x+11\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}B\left(x\right)=\dfrac{2}{3}x^2-\dfrac{5}{3}x-\dfrac{7}{3}\\A\left(x\right)=-x^2+4x+11+\dfrac{2}{3}x^2-\dfrac{5}{3}x-\dfrac{7}{3}=-\dfrac{1}{3}x^2+\dfrac{7}{3}x+\dfrac{26}{3}\end{matrix}\right.\)