An algebra problem by me...

Algebra Level 3

a+b+c=1a + b + c=1 , a2+b2+c2=9a^{2} + b^{2} + c^{2}=9 , a3+b3+c3=1a^{3} + b^{3} + c^{3}=1, then find 1a+1b+1c\frac{1}{a} +\frac{1}{b} + \frac{1}{c}

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