Đáp án:
B1:
\(P = 5\)
Giải thích các bước giải:
\(\begin{array}{l}
B1:\\
P = \dfrac{{\sqrt x + 3}}{{\sqrt x - 1}}\\
Thay:x = 4\\
\to P = \dfrac{{\sqrt 4 + 3}}{{\sqrt 4 - 1}} = \dfrac{{2 + 3}}{{2 - 1}} = 5\\
B2:\\
P = \dfrac{{\sqrt x + 1}}{{\sqrt x - 3}}\\
Thay:x = 100\\
\to P = \dfrac{{\sqrt {100} + 1}}{{\sqrt {100} - 3}} = \dfrac{{10 + 1}}{{10 - 3}} = \dfrac{{11}}{7}\\
B3:\\
P = \dfrac{{\sqrt x + 1}}{{\sqrt x - 3}}\\
Thay:x = 4 - 2\sqrt 3 = 3 - 2\sqrt 3 .1 + 1\\
= {\left( {\sqrt 3 - 1} \right)^2}\\
\to P = \dfrac{{\sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} + 1}}{{\sqrt {{{\left( {\sqrt 3 - 1} \right)}^2}} - 3}} = \dfrac{{\sqrt 3 - 1 + 1}}{{\sqrt 3 - 1 - 3}}\\
= \dfrac{{\sqrt 3 }}{{\sqrt 3 - 4}}\\
B4:\\
Thay:x = 14 - 6\sqrt 5 = 9 - 2.3.\sqrt 5 + 5\\
= {\left( {3 - \sqrt 5 } \right)^2}\\
\to P = \dfrac{{4\sqrt {{{\left( {3 - \sqrt 5 } \right)}^2}} - 3}}{{\sqrt {{{\left( {3 - \sqrt 5 } \right)}^2}} + 2}}\\
= \dfrac{{4\left( {3 - \sqrt 5 } \right) - 3}}{{\left( {3 - \sqrt 5 } \right) + 2}} = \dfrac{{ - 4\sqrt 5 + 9}}{{5 - \sqrt 5 }}
\end{array}\)
