Задача 30. Найдите   \(\frac{{p\left( b \right)}}{{p\left( {\frac{1}{b}} \right)}}\),   если   \(p\left( b \right) = \left( {b + \frac{3}{b}} \right)\left( {3b + \frac{1}{b}} \right)\)   при  \(b \ne 0\).

Ответ

ОТВЕТ: 1.

Решение

\(p\left( {\frac{1}{b}} \right) = \left( {\frac{1}{b} + \frac{3}{{\frac{1}{b}}}} \right)\left( {3 \cdot \frac{1}{b} + \frac{1}{{\frac{1}{b}}}} \right) = \left( {\frac{1}{b} + 3b} \right)\left( {\frac{3}{b} + b} \right)\)

\(\frac{{p\left( b \right)}}{{p\left( {\frac{1}{b}} \right)}} = \frac{{\left( {b + \frac{3}{b}} \right)\left( {3b + \frac{1}{b}} \right)}}{{\left( {\frac{1}{b} + 3b} \right)\left( {\frac{3}{b} + b} \right)}} = 1.\)

Ответ: 1.