Question

\(\sqrt{x-3}+5=\sqrt{7-x}+x\)

Answer 1

giải pt

Answer 2

ĐKXĐ: \(7\ge x\ge3\).

\(PT\Leftrightarrow\sqrt{x-3}-\sqrt{7-x}=x-5\)

\(\Leftrightarrow\dfrac{2x-10}{\sqrt{x-3}+\sqrt{7-x}}=x-5\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\left(TMĐK\right)\\\sqrt{x-3}+\sqrt{7-x}=2\left(1\right)\end{matrix}\right.\).

\(\left(1\right)\Leftrightarrow4+2\sqrt{\left(x-3\right)\left(7-x\right)}=4\)

\(\Leftrightarrow (x-3)(7-x)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(TMĐK\right)\\x=7\left(TMĐK\right)\end{matrix}\right.\).

Vậy nghiệm của pt là \(x\in\left\{3;5;7\right\}\).