Olympiad Mathematic | if 1/a+1/b+1/c=1/(a+b+c) prove 1/a^n+1/b^n+1/c^n=1/(a^n+b^n+c^n) for all odd n

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If 1/a + 1/b + 1/c = 1/(a + b + c)Then prove that 1/a^n + 1/b^n + 1/c^n = 1/(a + b + c)^n, n is oddIf 1/a + 1/b + 1/c = 1/(a + b + c)Then prove that 1/a^n + 1/b^n + 1/c^n = 1/(a + b + c)^n, n is odd
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What can you get from 1/a+1/b+1/c=1/(a+b+c)What can you get from 1/a+1/b+1/c=1/(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).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).