The greatest integer function, ⌊x⌋, is equal to the largest integer that is smaller than or equal to x. In the domain [0,100], how many solutions are there to
x^2−[x]x=82.25

Question

The greatest integer function, ⌊x⌋, is equal to the largest integer that is smaller than or equal to x. In the domain [0,100], how many solutions are there to
x^2−[x]x=82.25

dls · Answer

x(x-[x])=82.25
x({x}) = 82.25
what now?

dls · Answer

@ganeshie8 @hartnn

ganeshie8 · Answer

x^2−[x]x=82.25

divide x thru out

ganeshie8 · Answer

x - [x] = 82.5/x

ganeshie8 · Answer

observe that left side is (0, 1)

also see that, right side is >=1, when x <= 82.5

ganeshie8 · Answer

so our solutions will be very few numbers between  82.5 and 100

ganeshie8 · Answer

17 or 18 should be the # of solutions,
a careful observation gives u the exact count