How can I solve this equation for $(x,y)$?
$$\lfloor|x|\rfloor+\lfloor |y|\rfloor=3$$
Can you help me? Thanks.
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What does $[a]$ mean? – Git Gud Sep 29 '13 at 10:55
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$[a]$ is greatest integer function. – Sep 29 '13 at 10:58
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Do you mean the floor function? – Git Gud Sep 29 '13 at 11:02
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Oh, yes floor function. – Sep 29 '13 at 11:04
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I edited the question to include a more common notation. – Git Gud Sep 29 '13 at 11:05
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What have you already tried? – user93089 Sep 29 '13 at 11:11
2 Answers
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The equation is symmetrical in all Quadrant because $f(x,y) = f(-x,y) = f(x,-y) = f(x,y)$
where $f(x,y) = \lfloor |x|\rfloor +\lfloor |y|\rfloor - 3 = 0$
So I have calculate here for only $\bf{(I^{st})}$ Quadrant.
Given :: $\lfloor |x|\rfloor +\lfloor |y|\rfloor = 3$
$\bullet $ If $\lfloor |x|\rfloor =0$ and $\lfloor |y|\rfloor = 3$
Then $0<|x|<1$ and $3 \leq |y|<4$
$\bullet $ If $\lfloor |x|\rfloor =1$ and $\lfloor |y|\rfloor = 2$
Then $1\leq |x|<2$ and $2 \leq |y|<3$
$\bullet $ If $\lfloor |x|\rfloor =2$ and $\lfloor |y|\rfloor = 1$
Then $2\leq |x|<3$ and $1 \leq |y|<2$
$\bullet $ If $\lfloor |x|\rfloor =3$ and $\lfloor |y|\rfloor = 0$
Then $3\leq |x|<4$ and $0< |y|<1$
Now you will find Corrosponding Intervals for $x$ and $y$
Similarly for other $3$ Quadrants.
juantheron
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