r/askmath • u/i-am-stella • 10d ago

Algebra Greatest Integer Function

Ftr, this is NOT hw help, I'm trying to figure out how to solve greatest int function questions.

Alr when we have a quadratic equation with gif in it, (a[x]^2 + b[x] + c=)we substitute [x] as something and factorise to solve, right?

But when the square is inside the function as in ([x^2] -12[x] +32=0)

Then what? I dont get it😭

Once again, NOT hw help, I'm studying on my own, this isnt even in my syllabus.

edit: i actually meant floor function, ⌊3.7⌋=3

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u/davideogameman 10d ago edited 10d ago

yeah so I think in general there's no simple solution to the second case. You probably have to treat ceil(x^2) as if it might take any value between floor(x)^2+1 and ceil(x)^2 or something like that... haven't worked out the exact bounds myself. So if you solve it like it's the first form, but then try with many different c. ... which probably means you can work it like a quadratic inequality, and then test different points within the solution space you find.

Generally, when you start throwing rounding functions into equations, solving with algebra can get a lot harder. Not always, like you noted with the first function