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NL-NWO 1986 Problem 1

    f(x)=12x+919x+86, x≠−8619f(x) = \frac{12x+9}{19x+86}, \, x \ne -\frac{86}{19} Prove that ∃!  xo∈R  ∀h1,h2∈R[f(x0+h1)f(x0−h1)=f(x0+h2)f(x0−h2)]\exists ! \,\, {x_o \in R} \,\, \forall h_1,h_2 \in R [f(x_0+h_1)f(x_0-h_1)=f(x_0+h_2)f(x_0-h_2)] , and calculate x0x_0 .

    Dataset text AI-MO AoPS. Quoted with source.

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