HSG lớp 8?

P

pinkylun

ĐỀ đúng là:

$\dfrac{ab+1}{b}=\dfrac{bc+1}{c}=\dfrac{ac+1}{a}$

$=>a+\dfrac{1}{b}=b+\dfrac{1}{c}=c+\dfrac{1}{a}$

$=>a-b=\dfrac{b-c}{bc}$ (1)

$b-c=\dfrac{c-a}{ac}$ (2)

$c-a=\dfrac{a-b}{ab}$ (3)

(1),(2),(3) nhân vế theo vế

$=>(a-b)(b-c)(c-a)=\dfrac{(a-b)(b-c)(c-a)}{a^2b^2c^2}$

..... chuyển vế đặt chung

mà abc khác 1 =>$a^2b^2c^2$ khác 1

$=>(a-b)(b-c)(c-a)=0=>a=b=c$
 
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