High school mathematics problem f (x) = x ^ 2-2lnx, G (x) = x-2x ^ 0.5 verification: when x is greater than 0, f (x) = g (x) + 2 has a unique solution f（x）=x^2-2Lnx,g（x）=x-2x^0.5 It is proved that f (x) = g (x) + 2 has a unique solution when x is greater than 0

In order to prove that f (x) = g (x) + 2 has a unique solution, as long as there is only one intersection point in the function image of the two sides of the equation. Prove: ∵ f (x) = x ^ 2-2lnx, G (x) = x-2x ^ 0.5 let H (x) = x ^ 2-2lnx - x + 2x ^ 0.5-2 let H '(x) = 2x-2 / X-1 + x ^ (- 0.5) = [2x ^ 2-x-x ^ (0.5) - 2] / x = 0 let t = x ^ (0.5) (t

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