Question

Алгебра, 441 с 1-2 (10 баллов)​

Answer 1

$A^2_m=90\Leftrightarrow \frac{m!}{(m-2)!}=90\Leftrightarrow \frac{m(m-1)(m-2)!}{(m-2)!}=90\\m^2-m-90=0\Rightarrow m=\left \{ -9;10 \right \}$

$A_m^3=56m\Leftrightarrow \frac{m!}{(m-3)!}=56m\Leftrightarrow \frac{m(m-1)(m-2)(m-3)!}{(m-3)!}=56m\\ m^3-3m^2+2m=56m\\m^3-3m^2-54m=0\Leftrightarrow m(m^2-3m-54)=0\Rightarrow m=\left \{ -6;0;9 \right \}$