a: \(\left\{{}\begin{matrix}M\left(x\right)+N\left(x\right)=2x^2+4\\M\left(x\right)-N\left(x\right)=6x\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2\cdot M\left(x\right)=2x^2+6x+4\\M\left(x\right)-N\left(x\right)=6x\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}M\left(x\right)=x^2+3x+2\\N\left(x\right)=M\left(x\right)-6x=x^2+3x+2-6x=x^2-3x+2\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}M\left(x\right)+N\left(x\right)=5x^4-6x^3-3x^2-4\\M\left(x\right)-N\left(x\right)=3x^4+7x^2+8x+2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2M\left(x\right)=5x^4-6x^3-3x^2-4+3x^4+7x^2+8x+2\\M\left(x\right)-N\left(x\right)=3x^4+7x^2+8x+2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2M\left(x\right)=8x^4-6x^3+4x^2+8x+2\\M\left(x\right)-N\left(x\right)=3x^4+7x^2+8x+2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}M\left(x\right)=4x^4-3x^3+2x^2+4x+1\\N\left(x\right)=4x^4-3x^3+2x^2+4x+1-3x^4-7x^2-8x-2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}M\left(x\right)=4x^4-3x^3+2x^2+4x+1\\N\left(x\right)=x^4-3x^3-5x^2-4x-1\end{matrix}\right.\)
