a+b \geq
c \geq
b+1 \Leftrightarrow
a \geq
1
Mà
b \geq
a \Leftrightarrow
b\geq1
\Rightarrow
(a−1)(b−1) \geq 0 \Leftrightarrow
ab+1\geq
a+b\geqc \Leftrightarrow
ab\geq
c−1
Có
Q\geq
(a+1)(b+1)(c−1)2ab+abc=(ab+a+b+1)(c+1)ab(c+2)
\Rightarrow
Q \geq
2(ab+1)(c+1)ab(c+2)=2(1+ab1)(c+1)c+2
\Rightarrow
Q \geq
2(1+c−11)(c+1)c+2=2c(c+1)(c+2)(c−1)
\Leftrightarrow
Q \geq
2(c2+c)c2+c−2=21−c2+c1
\Leftrightarrow
Q \geq
21−32+31=125