Đáp án:
c) x=100
Giải thích các bước giải:
\(\begin{array}{l}
a)P = \dfrac{{\left( {6\sqrt x + 1} \right)\left( {\sqrt x - 2} \right) + \left( {\sqrt x - 4} \right)\left( {\sqrt x + 10} \right) - 6x + 15\sqrt x + 42}}{{\left( {\sqrt x + 10} \right)\left( {\sqrt x - 2} \right)}}\\
= \dfrac{{6x - 11\sqrt x - 2 + x + 6\sqrt x - 40 - 6x + 15\sqrt x + 42}}{{\left( {\sqrt x + 10} \right)\left( {\sqrt x - 2} \right)}}\\
= \dfrac{{x + 10\sqrt x }}{{\left( {\sqrt x + 10} \right)\left( {\sqrt x - 2} \right)}} = \dfrac{{\sqrt x }}{{\sqrt x - 2}}\\
b)Thay:x = 16\\
\to P = \dfrac{{\sqrt {16} }}{{\sqrt {16} - 2}} = \dfrac{4}{2} = 2\\
c)P = \dfrac{5}{4}\\
\to \dfrac{{\sqrt x }}{{\sqrt x - 2}} = \dfrac{5}{4}\\
\to 5\sqrt x - 10 = 4\sqrt x \\
\to \sqrt x = 10\\
\to x = 100
\end{array}\)
