Question

Tìm x, y biết:

a) \(2^{x+1}.5^y=20^x\)

b) \(\left(2x-1\right)^4+\left(3y-6\right)^2\le0\)

Answer 1

\(\left(2x-1\right)^4+\left(3y-6\right)^2\le0\)

\(\left\{{}\begin{matrix}\left(2x-1\right)^4\ge0\forall x\\\left(3y-6\right)^2\ge0\forall y\end{matrix}\right.\)

\(\Rightarrow\left(2x-1\right)^4+\left(3y-6\right)^2\ge0\)

\(\Rightarrow\left[{}\begin{matrix}\left(2x-1\right)^4+\left(3y-6\right)^2\ge0\\\left(2x-1\right)^4+\left(3y-6\right)^2\le0\end{matrix}\right.\)

\(\Rightarrow\left(2x-1\right)^4+\left(3y-6\right)^2=0\)

Dấu "=" xảy ra khi:

\(\left\{{}\begin{matrix}\left(2x-1\right)^4=0\Rightarrow2x=1\Rightarrow x=\dfrac{1}{2}\\\left(3y-6\right)^2=0\Rightarrow3y=6\Rightarrow y=2\end{matrix}\right.\)