Đáp án:
\(x = 3,32760833\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x > 0\\
P = \dfrac{{\sqrt x + 1}}{{\sqrt x }}\\
P.\sqrt x = 6\sqrt x - 3\sqrt {x + 4} \\
\to \dfrac{{\sqrt x + 1}}{{\sqrt x }}.\sqrt x = 6\sqrt x - 3\sqrt {x + 4} \\
\to \sqrt x + 1 = 6\sqrt x - 3\sqrt {x + 4} \\
\to 3\sqrt {x + 4} = 5\sqrt x - 1\\
\to 9\left( {x + 4} \right) = 25x - 10\sqrt x + 1\\
\to 16x - 10\sqrt x - 35 = 0\\
\Delta ' = 25 - 16.\left( { - 35} \right) = 585\\
\to \left[ \begin{array}{l}
\sqrt x = \dfrac{{5 + 3\sqrt {65} }}{{16}}\\
\sqrt x = \dfrac{{5 - 3\sqrt {65} }}{{16}}\left( l \right)
\end{array} \right.\\
\to x = 3,32760833
\end{array}\)
