Задача 85. Найдите  \(\dfrac{{p\left( b \right)}}{{p\left( {\dfrac{1}{b}} \right)}}\),  если  \(p\left( b \right) = \left( {b-\dfrac{7}{b}} \right)\left( {-7b + \dfrac{1}{b}} \right)\)   при  \(b \ne 0\)

Ответ

ОТВЕТ: 1.

Решение

\(p\left( {\dfrac{1}{b}} \right) = \left( {\dfrac{1}{b}-\dfrac{7}{{\dfrac{1}{b}}}} \right)\left( {-\dfrac{7}{b} + \dfrac{1}{{\dfrac{1}{b}}}} \right) = \left( {\dfrac{1}{b}-7b} \right)\left( {-\dfrac{7}{b} + b} \right).\)

\(\dfrac{{p\left( b \right)}}{{p\left( {\dfrac{1}{b}} \right)}} = \dfrac{{\left( {b-\dfrac{7}{b}} \right)\left( {-7b + \dfrac{1}{b}} \right)}}{{\left( {\dfrac{1}{b}-7b} \right)\left( {-\dfrac{7}{b} + b} \right)}} = 1.\)

Ответ:  1.