Algebra-All zebras meeting spot

Algebra Level 3

If x+1x=1 x + \frac{1}{x} = 1 , then find the value of

x+x4+x7+x10+x19+x22+x25+x31+x34+x40. x+{ x }^{ 4 }+{ x }^{ 7 }+{ x }^{ 10 }+{ x }^{ 19 }+{ x }^{ 22 }+{ x }^{ 25 }+{ x }^{ 31 }+{ x }^{ 34 }+{ x }^{ 40 }.

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