Math Olympiad - Algebra Problem | If a + 1/b = 1 , b + 1/c = 1 Then c + 1/a =?

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If GCD(a, b, c)=1 and (1/a+1/b = 1/c) then (a+b) is perfect square If GCD(a, b, c)=1 and (1/a+1/b = 1/c) then (a+b) is perfect square
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If 1/a+1/b+1/(a+x)=0, 1/a+1/c+1/(a+y)=0 and 1/a+1/x+1/y=0, where a≠0, b≠0, c≠0, find (a+b+c). If 1/a+1/b+1/(a+x)=0, 1/a+1/c+1/(a+y)=0 and 1/a+1/x+1/y=0, where a≠0, b≠0, c≠0, find (a+b+c).
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