\(A=2y\cdot\sqrt{\dfrac{x^4}{4y^2}}\)
\(=2y\cdot\sqrt{\left(\dfrac{x^2}{2y}\right)^2}\)
\(=2y\cdot\dfrac{x^2}{\left|2y\right|}\)
Vì y<0 nên 2y<0
=>\(A=2y\cdot\dfrac{x^2}{-2y}=-x^2\)
A+x+6=0
=>\(-x^2+x+6=0\)
=>\(x^2-x-6=0\)
=>(x-3)(x+2)=0
=>\(\left[{}\begin{matrix}x-3=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
Giá trị x nguyên âm thỏa mãn là -2