If a^b=b^c=a×b, then what is the value a+b ?
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➡️ ab+c=ba+cab+c=ba+c
⟹a(a+c)=b(b+c)⟹a(a+c)=b(b+c)
⟹a2+ac=b2+bc⟹a2+ac=b2+bc
⟹a2−b2=c(b−a)⟹a2−b2=c(b−a)
⟹(a−b)(a+b)=c(b−a)⟹(a−b)(a+b)=c(b−a)
⟹(a+b)=−c⟹(a+b)=−c or a=ba=b
➡️ ab+c=ba+cab+c=ba+c
⟹a(a+c)=b(b+c)⟹a(a+c)=b(b+c)
⟹a2+ac=b2+bc⟹a2+ac=b2+bc
⟹a2−b2=c(b−a)⟹a2−b2=c(b−a)
⟹(a−b)(a+b)=c(b−a)⟹(a−b)(a+b)=c(b−a)
⟹(a+b)=−c⟹(a+b)=−c or a=ba=b
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