Question

\(\left\{{}\begin{matrix}\dfrac{1}{\sqrt{x-1}}+2\left|3y-2\right|=5\\\dfrac{5}{\sqrt{x-1}}-\left|3y-2\right|=3\end{matrix}\right.\)

Answer 1

ĐKXĐ: x>1

\(\left\{{}\begin{matrix}\dfrac{1}{\sqrt{y-1}}+2\left|3y-2\right|=5\\\dfrac{5}{\sqrt{x-1}}-\left|3y-2\right|=3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\dfrac{1}{\sqrt{x-1}}+2\left|3y-2\right|=5\\\dfrac{10}{\sqrt{x-1}}-2\left|3y-2\right|=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{11}{\sqrt{x-1}}=11\\\dfrac{5}{\sqrt{x-1}}-\left|3y-2\right|=3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}\sqrt{x-1}=1\\\left|3y-2\right|=5-3=2\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x-1=1\\3y-2\in\left\{2;-2\right\}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=2\\y\in\left\{\dfrac{4}{3};0\right\}\end{matrix}\right.\left(nhận\right)\)