Question

can somebody explain me to draw graphs of equations like [x]+[y]=5 as fast as possible?

Answer 1

[x] is the box function also known as the greatest integer function..

Answer 2

for starting ideas..i was thinking of plotting some particular points like (5,0),(0,5),(3,2),(2,3),(1,4),(4,1)..

Answer 3

then I would probably think of the non-integers..for non-integers say in [0,1) we have [x]=0 so [y]=5 is needed which means [5,6) is the range of y..

Answer 4

now, hence we get a rectangle with x-coordinates in [0,1) and y-coordinates in [5,6)..the whole region i.e. the whole set of points within the rectangle must be satisfying the equation..

Answer 5

similarly for any x in [n,n+1) we get a rectangle with y in [n+5,n+6) and the points in/on the rectangle satisfy the equation...

Answer 6

for negative x say in [-1,0), [x]=-1 so [y]=6 which means y will vary from [6,7). So for x in [n,n+1)...(n being negative)...we have y in
[|n|+5,|n|+6).
Lets check this:
if x lies in [-2,-1) we have, [x]=-2 so [y]=7 which means y will vary from [7,8).[|-2|+5,|-2|+6)=[7,8)...

Answer 7

So our graph is done...:)
But i seek more shorter ways..any tricks,insights,ideas :)

Answer 8

If [x]=n, i.e n<=x<n+1 then [y]=5-n. So 5-n<=y < 4-n

Answer 9

It's gonna look like the attached graph. :)

Answer 10

can somebody explain how to factorize the equation x^4+x^3-2x^2-6ax-4a^2=0