a+b=b+c=a+c=abc (a,b,c)=?


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Question Number 173115 by dragan91 last updated on 06/Jul/22

$a + b = b + c = a + c = abc$ $(a, b, c) = ?$
Commented by kaivan.ahmadi last updated on 06/Jul/22
$a+b=b+c⇒a=c a+b=a+c⇒b=c ⇒a=b=c=x 2x=x^3 ⇒x^3 −2x=0⇒x(x^2 −2)=0⇒ {_(x^2 =2⇒x=±(√2)) ^(x=0)$
$a + b = b + c \Rightarrow a = c$ $a + b = a + c \Rightarrow b = c$ $\Rightarrow a = b = c = x$ $2 x = x^{3} \Rightarrow x^{3} - 2 x = 0 \Rightarrow x (x^{2} - 2) = 0 \Rightarrow$ ${_{x^{2} = 2 \Rightarrow x = \pm \sqrt{2}}^{x = 0}$
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