Đáp án:
P<1
Giải thích các bước giải:
\(\begin{array}{l}
M = \dfrac{{2\sqrt x \left( {\sqrt x + 3} \right) - x - 9\sqrt x }}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}\\
= \dfrac{{2x + 6\sqrt x - x - 9\sqrt x }}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}\\
= \dfrac{{x - 3\sqrt x }}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}\\
= \dfrac{{\sqrt x }}{{\sqrt x + 3}}\\
P = M.N = \dfrac{{\sqrt x }}{{\sqrt x + 3}}:\dfrac{{\sqrt x }}{{\sqrt x - 5}}\\
= \dfrac{{\sqrt x - 5}}{{\sqrt x + 3}}\\
c)Xét:P - 1 = \dfrac{{\sqrt x - 5}}{{\sqrt x + 3}} - 1\\
= \dfrac{{\sqrt x - 5 - \sqrt x - 3}}{{\sqrt x + 3}}\\
= \dfrac{{ - 8}}{{\sqrt x + 3}}\\
Do:\sqrt x + 3 > 0\forall x > 0\\
\to \dfrac{{ - 8}}{{\sqrt x + 3}} < 0\\
\to P - 1 < 0\\
\to P < 1
\end{array}\)
