- #1

Mentallic

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[tex]y=\left(x^2-6x+8+\sqrt{x^4-12x^3+52x^2-96x+64}\right)^2[/tex]

It seems that there is a root y=0 for the domain x=[2,4].

I've never seen such weird behaviour on a graph before. How could analysis of this function (or not?) determine that there is a root for all values [itex]2\leq x\leq 4[/itex]?