Упрощение алгебраических выражений. Задача 86math100admin44242025-03-27T09:02:32+03:00
Задача 86. Найдите \(\dfrac{{p\left( b \right)}}{{p\left( {\dfrac{1}{b}} \right)}}\), если \(p\left( b \right) = \left( {b-\dfrac{{10}}{b}} \right)\left( {-10b + \dfrac{1}{b}} \right)\) при \(b \ne 0\)
Решение
\(p\left( {\dfrac{1}{b}} \right) = \left( {\dfrac{1}{b}-\dfrac{{10}}{{\dfrac{1}{b}}}} \right)\left( {-\dfrac{{10}}{b} + \dfrac{1}{{\dfrac{1}{b}}}} \right) = \left( {\dfrac{1}{b}-10b} \right)\left( {-\dfrac{{10}}{b} + b} \right).\)
\(\dfrac{{p\left( b \right)}}{{p\left( {\dfrac{1}{b}} \right)}} = \dfrac{{\left( {b-\dfrac{{10}}{b}} \right)\left( {-10b + \dfrac{1}{b}} \right)}}{{\left( {\dfrac{1}{b}-10b} \right)\left( {-\dfrac{{10}}{b} + b} \right)}} = 1.\)
Ответ: 1.