Đáp án:
P=27
Giải thích các bước giải:
\(\begin{array}{l}\lim \dfrac{{\sqrt[3]{{a{n^3} + 5{n^2} - 7}}}}{{\sqrt {3{n^2} - n + 2} }} = \lim \dfrac{{n\sqrt[3]{{a + \dfrac{5}{n} - \dfrac{7}{{{n^3}}}}}}}{{n\sqrt {3 - \dfrac{1}{n} + \dfrac{2}{{{n^2}}}} }}\\ = \lim \dfrac{{\sqrt[3]{{a + \dfrac{5}{n} - \dfrac{7}{{{n^3}}}}}}}{{\sqrt {3 - \dfrac{1}{n} + \dfrac{2}{{{n^2}}}} }} = \dfrac{{\sqrt[3]{{a + 0 - 0}}}}{{\sqrt {3 - 0 + 0} }} = \dfrac{{\sqrt[3]{a}}}{{\sqrt 3 }} = \dfrac{{\sqrt[3]{a}}}{3}.\sqrt 3 \end{array}\)
\( \Rightarrow b = \dfrac{{\sqrt[3]{a}}}{3},c = 0 \Rightarrow P = \dfrac{{a + c}}{{{b^3}}} = \dfrac{{a + 0}}{{\dfrac{a}{{27}}}} = 27\)
