Question

Найдите значение выражения , если p(b)=(b+6/b)*(6b+1/b)

Answer 1

$p(b)= \frac{b+\frac{6}{b}}{6b+\frac{1}{b}} \\\\p(\frac{1}{b})= \frac{\frac{1}{b}+6b}{\frac{6}{b}+b} =\frac{1}{p(b)}\\\\ \frac{p(b)}{p(\frac{1}{b})} = \frac{p(b)}{1/p(b)} =p^2(b)=\left (\frac{b+\frac{6}{b}}{6b+\frac{1}{b}}\right )^2=\left (\frac{b^2+6}{6b^2+1}\right )^2= \frac{b^4+12b^2+36}{36b^4+12b^2+1}$