Question

. Xác định hệ số a, b, c biết:

a, ( ax + 1 )( ax + b) = x² + 7

b, ( ax + b )( x² + cx + 1 ) = x³ - 3x + 2.

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Answer 1

a: \(\left(ax+1\right)\left(ax+b\right)=x^2+7\)

\(\Leftrightarrow a^2x^2+abx+ax+b=x^2+7\)

\(\Leftrightarrow a^2x^2+ax\left(b+1\right)+b=x^2+7\)

\(\Leftrightarrow\left\{{}\begin{matrix}a^2=1\\b=7\\a\left(b+1\right)=0\end{matrix}\right.\Leftrightarrow\left(a,b\right)\in\varnothing\)

b: \(\Leftrightarrow ax^3+acx^2+ax+x^2b+cxb+b=x^3-3x+2\)

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

\(\Leftrightarrow\left\{{}\begin{matrix}a=1\\ac+b=0\\a+bc=3\\b=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=1\\b=2\\c+2=0\\1+2\cdot\left(-2\right)=3\end{matrix}\right.\Leftrightarrow\left(a,b,c\right)\in\varnothing\)