Đáp án: $A=24$
Giải thích các bước giải:
Ta có:
$\dfrac{2000a-b-c}{a}=\dfrac{2000b-a-c}{b}=\dfrac{2000c-a-b}{c}$
$\to 2000+\dfrac{-b-c}{a}=2000+\dfrac{-a-c}{b}=2000+\dfrac{-a-b}{c}$
$\to \dfrac{-b-c}{a}=\dfrac{-a-c}{b}=\dfrac{-a-b}{c}$
$\to \dfrac{b+c}{a}=\dfrac{a+c}{b}=\dfrac{a+b}{c}$
$\to \dfrac{b+c}{a}+1=\dfrac{a+c}{b}+1=\dfrac{a+b}{c}+1$
$\to\dfrac{a+b+c}{a}=\dfrac{a+b+c}{b}=\dfrac{a+b+c}{c}$
Vì $a,b,c>0\to a+b+c>0$
$\to a=b=c$
$\to A=(1+\dfrac{a}a)(2+\dfrac{a}a)(3+\dfrac{a}a)$
$\to A=2\cdot 3\cdot 4$
$\to A=24$
