Question

решить уравнение

(m+1)!/(m-1)!=30

Answer 1

 

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