Question

решить уравнение(m+1)!/(m-1)!=30

Answer 1

 

$\frac{(m+1)!}{(m-1)!} = 30\\\\ \frac{1*2*...*(m-1)*m*(m+1)}{1*2*...*(m-1)} = 30\\\\ m*(m+1) = 30\\\\ m^2+m - 30 = 0\\\\ m_1*m_2 = -30 = 5*(-6)\\ m_1+m_2 = -1 = 5 - 6\\\\ m_1 = 5,\\ m_2 = -6 < 0\\\\ \fbox{m = 5}$