Question

GHPT: \(\left\{{}\begin{matrix}2x+3+\sqrt{4-y}=4\\2y+3+\sqrt{4-x}=4\end{matrix}\right.\)

Answer 1

ĐKXĐ: ...

Trừ vế cho vế:

\(2\left(x-y\right)+\sqrt{4-y}-\sqrt{4-x}=0\)

\(\Leftrightarrow2\left(x-y\right)+\dfrac{x-y}{\sqrt{4-y}+\sqrt{4-x}}=0\)

\(\Leftrightarrow\left(x-y\right)\left(2+\dfrac{1}{\sqrt{4-y}+\sqrt{4-x}}\right)=0\)

\(\Leftrightarrow x=y\)

Thế vào pt đầu:

\(2x+3+\sqrt{4-x}=4\)

\(\Leftrightarrow\sqrt{4-x}=1-2x\) (\(x\le\dfrac{1}{2}\))

\(\Leftrightarrow4-x=1-4x+4x^2\)

\(\Leftrightarrow4x^2-3x-3=0\)

\(\Leftrightarrow..\)