\(7^{2x-6}=49\)

\(\Rightarrow7^{2x-6}=7^2\)

\(\Rightarrow2x-6=2\)

\(\Rightarrow2x=2+6\)

\(\Rightarrow2x=8\)

\(\Rightarrow x=8:2=4\)

Ta thấy: \(\left(x-y+3\right)^2\ge0\forall x;y\)

              \(\left|y-3\right|\ge0\forall y\)

\(\Rightarrow\left(x-y+3\right)^2+\left|y-3\right|\ge0\forall x;y\)

Mặt khác: \(\left(x-y+3\right)^2+\left|y-3\right|\le0\)

\(\Rightarrow\left(x-y+3\right)^2+\left|y-3\right|=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-y+3\right)^2=0\\y-3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-y+3=0\\y=3\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-3+3=0\\y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=3\end{matrix}\right.\)

Khi đó, biểu thức \(\left(x-2y+6\right)^{10}+27\) trở thành:

\(\left(0-2\cdot3+6\right)^{10}+27\)

\(=\left(-6+6\right)^{10}+27\)

\(=27\)

#Urushi