Question

Tìm a, b, c biết

1) 3x² (ax²-2bx-3c)=3x⁴-12x³+27x²

2) x²+cx+2)(ax+b)=x³+x²-2

3) (ax²+bx+c)+(x+3)=x³+2x²-3x

 

Answer 1

1. \(3x^2\left(ax^2-2bx-3c\right)=3x^2\left(x^2-4x+27\right)\)

\(\Rightarrow\hept{\begin{cases}a=1\\-2b=-4\\-3c=27\end{cases}\Rightarrow\hept{\begin{cases}a=1\\b=2\\c=-9\end{cases}}}\)

2. \(\left(x^2+cx+2\right)\left(ax+b\right)=x^3+x^2-2\)

\(\Rightarrow ax^3+bx^2+acx^2+bcx+2ax+2b=x^3+x^2-2\)

\(\Rightarrow ax^3+\left(b+ac\right)x^2+\left(bc+2a\right)x+2b=x^3+x^2-2\)

\(\Rightarrow\hept{\begin{cases}a=1\\b+ac=1\\2b=-2\end{cases}\Rightarrow\hept{\begin{cases}a=1\\b+ac=1\\b=-1\end{cases}\Rightarrow}\hept{\begin{cases}a=1\\b=-1\\c=2\end{cases}}}\)

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