Question

tìm x và y biết : (x-5)\(^8\)+ \(\left|y^2-4\right|\)= 0

Answer 1

Do \(\left\{{}\begin{matrix}\left(x-5\right)^8\ge0\forall x\\\left|y^2-4\right|\ge0\forall y\end{matrix}\right.\)

\(\Rightarrow\left(x-5\right)^8+\left|y^2-4\right|=0\Leftrightarrow\left\{{}\begin{matrix}\left(x-5\right)^8=0\\\left|y^2-4\right|=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-5=0\\\left(y-2\right)\left(y+2\right)=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=5\\\left[{}\begin{matrix}y=2\\y=-2\end{matrix}\right.\end{matrix}\right.\)

Vậy pt đã cho có hai cặp nghiệm \(\left(x;y\right)=\) \(\left(5;2\right)\) và \(\left(5;-2\right)\)