Giải thích các bước giải:
Ta có:
$m^2+n^2+p^2+q^2+1$
$=(\dfrac{m^2}{4}+1)+(\dfrac{m^2}{4}+n^2)+(\dfrac{m^2}{4}+p^2)+(\dfrac{m^2}{4}+q^2)$
$=((\dfrac{m}{2})^2+1)+((\dfrac{m}{2})^2+n^2)+((\dfrac{m}{2})^2+p^2)+((\dfrac{m}{2})^2+q^2)$
$\ge 2\cdot\dfrac{m}{2}\cdot 1+2\cdot\dfrac{m}{2}\cdot n+2\cdot\dfrac{m}{2}\cdot p+2\cdot\dfrac{m}{2}\cdot q$
$\ge m+mn+mp+mq$
$=m(1+n+p+q)$
$\to m^2+n^2+p^2+q^2+1\ge m(n+p+q+1)$