a/ \(x^4+y^4=1\Rightarrow\left\{{}\begin{matrix}x^4\le1\\y^4\le1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\left|x\right|\le1\\\left|y\right|\le1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x^4\ge x^6\\y^4\ge y^6\end{matrix}\right.\) \(\Rightarrow x^6+y^6\le x^4+y^4\le1\)
Dấu "=" xảy ra khi và chỉ khi \(\left\{{}\begin{matrix}x^4=x^6\\y^4=y^6\\x^4+y^4=1\end{matrix}\right.\)
\(\Leftrightarrow\left(x;y\right)=\left(1;0\right);\left(0;1\right);\left(-1;0\right);\left(0;-1\right)\)
b/ \(\Rightarrow x^9+y^4=1.\left(x^4+y^4\right)\)
\(\Rightarrow x^9+y^9=\left(x^5+y^5\right)\left(x^4+y^4\right)\)
\(\Rightarrow x^9+y^9=x^9+y^9+x^5y^4+x^4y^5\)
\(\Rightarrow x^4y^4\left(x+y\right)=0\Rightarrow\left[{}\begin{matrix}xy=0\\x=-y\left(l\right)\end{matrix}\right.\)
\(\Rightarrow\left(x;y\right)=\left(0;1\right);\left(1;0\right)\)
