It is proved that the equation x ^ 5-3x = 1 has at least one root between 1 and 2 The answer should be detailed

Proof: Let f (x) = x ^ 5-3x-1
F (x) is continuous on interval [1,2]
f(1)=-30
From the inference of the intermediate value theorem,
There must be a point ξ in (1,2) such that f (ξ) = 0
This ξ is the root of the original equation

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