Đáp án:
$A(x)=2,5x^3+2,5x^2-2,5x+5$
$x=-2$
Giải thích các bước giải:
$M(x)=2,5x^3-0,5x-x^3-1=1,5x^3-0,5x-1\\
N(x)=-x^3-2,5x^2-6+2x\\
A(x)=M(x)-N(x)=1,5x^3-0,5x-1-(-x^3-2,5x^2-6+2x)\\
=1,5x^3-0,5x-1+x^3+2,5x^2+6-2x\\
=2,5x^3+2,5x^2-2,5x+5\\
A(x)=0\\
\Leftrightarrow 2,5x^3+2,5x^2-2,5x+5=0\\
\Leftrightarrow x^3+x^2-x+2=0\\
\Leftrightarrow x^3+2x^2-x^2-2x+x+2=0\\
\Leftrightarrow x^2(x+2)-x(x+2)+(x+2)=0\\
\Leftrightarrow (x+2)(x^2-x+1)=0\\
\Leftrightarrow {\left[\begin{aligned}x+2=0\\ x^2-x+1=0\end{aligned}\right.}\Leftrightarrow {\left[\begin{aligned}x=-2\\(x-\frac{1}{2})^2+\frac{3}{4}=0 (VN)\end{aligned}\right.}\Leftrightarrow x=-2$
