Question

XÁT ĐỊNH a,b,c BIẾT RẰNG:

a/\(-4x^{^{ }3}\cdot\left(ax^2+bx+c\right)=-8x^5+12x^4-20x^3\)

b/\(-2x^3\cdot\left(ax^2-bx-c\right)=-4x^5+6x^4+2x^3\)

Answer 1

a/ \(-4x^3\cdot\left(ax^2+bx+c\right)=-8x^5+12x^4-20x^3\)

\(\Leftrightarrow-4ax^5-4bx^4-4cx^3=-8x^5+12x^4-20x^3\)

\(\Leftrightarrow\left[{}\begin{matrix}a=-\dfrac{8}{-4}=\dfrac{8}{4}=2\\b=-\dfrac{12}{4}=-3\\c=-\dfrac{20}{-4}=5\end{matrix}\right.\)

Vậy......................

b/ \(-2x^3\cdot\left(ax^2-bx-c\right)=-4x^5+6x^4+2x^3\)

\(\Leftrightarrow-2ax^5+2bx^4+2cx^3=-4x^5+6x^4+2x^3\)

\(\Leftrightarrow\left[{}\begin{matrix}a=2\\b=3\\c=1\end{matrix}\right.\)