a)\(x^{2016}=x^{2017}\)

 \(\Leftrightarrow x^{2017}-x^{2016}=0\)

\(\Leftrightarrow x^{2016}.\left(x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x^{2016}=0\\x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}}\)

Vay ...

b) \(2y.\left(x+1\right)-x-7=0\)

\(\Leftrightarrow2y.\left(x+1\right)-\left(x+1\right)=6\)

\(\Leftrightarrow\left(x+1\right).\left(2y+1\right)=6\)

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\(x-2y=2x+2y\\ \Rightarrow x=-4y\left(1\right)\\ \Rightarrow\dfrac{x}{y}=-4\\ \Rightarrow x-y=-4\Rightarrow x=-4+y\left(2\right)\\ \left(1\right)\left(2\right)\Rightarrow-4+y=-4y\\ \Rightarrow-5y=-4\Rightarrow y=\dfrac{4}{5}\\ \Rightarrow x=-4\cdot\dfrac{4}{5}=-\dfrac{16}{5}\)

a, Vì \(\left|x-1\right|\ge0\)\(\forall x\inℤ\); \(\left|y+2\right|\)\(\forall y\inℤ\)

\(\Rightarrow\left|x-1\right|+\left|y+2\right|\ge0\)\(\forall x,y\inℤ\)

Dấu " = " xảy ra <=> \(\hept{\begin{cases}x-1=0\\y+2=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=1\\y=-2\end{cases}}\)

Vậy...

b, Vì \(\left|x+35-40\right|=\left|x-5\right|\ge0\)\(\forall x\inℤ\)

\(\left|y+10-x\right|\ge0\)\(\forall x,y\inℤ\)

\(\Rightarrow\left|x-5\right|+\left|y+10-x\right|\ge0\)\(\forall x,y\inℤ\)

Dấu " = " xảy ra <=> \(\hept{\begin{cases}x-5=0\\y+10-x=0\end{cases}}\Rightarrow\hept{\begin{cases}x=5\\y-x=-10\end{cases}}\Rightarrow\hept{\begin{cases}x=5\\y-5=-10\end{cases}}\Rightarrow\hept{\begin{cases}x=5\\y=-5\end{cases}}\)

Vậy...