Giải hệ: \(\left\{{}\begin{matrix}x+y-\dfrac{4}{x}-\dfrac{4}{y}=3\\x+y+\dfrac{6}{x+y}=-5\end{matrix}\right.\)

Giải hệ:

\(\left\{{}\begin{matrix}x^2+2y=xy+2x\\\sqrt{x+y}=xy-2\end{matrix}\right.\)

Giải hệ:

\(\left\{{}\begin{matrix}x^3+y^3=1\\x^2+y^5=x^3+y^2\end{matrix}\right.\)

\(x^7=x^2\Rightarrow x^7-x^2=0\)

\(\Rightarrow x^2\left(x^5-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2=0\\x^5=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

\(\left(a^4+a^3b+a^2b^2+ab^3+b^4\right)\left(a-b\right)\)

\(=a\left(a^4+a^3b+a^2b^2+ab^3+b^4\right)-b\left(a^4+a^3b+a^2b^2+ab^3+b^4\right)\)

\(=a^5+a^4b+a^3b^2+a^2b^3+ab^4-\left(ab^4+a^3b^2+a^2b^3+ab^4+b^5\right)\)

\(=a^5+a^4b+a^3b^2+a^2b^3+ab^4-ab^4-a^3b^2-a^2b^3-ab^4-b^5\)

\(=a^5-b^5\)