Solving a system of quadratic inequalities ⌊ c 2 ( x 2 + y 2 ) + 2 c ( x + y ) + 2 + 1 2 ⌋ = cFor a given positive integer c, I am trying to define algebraically, in terms of x &amp; y, the region in 2D space for which the above equation and the following conditions hold:1. c ∈ N2. 0 ≤ x , y ≤ 1I.E, which constraints/inequalities x &amp; y must fulfill (in terms of c)

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Solving a system of quadratic inequalities        ⌊              c      2        (          x      2        +          y      2        )    +    2    c    (    x    +    y    )    +    2    +      1    2          ⌋    =  cFor a given positive integer c, I am trying to define algebraically, in terms of   x &amp;amp;   y, the region in 2D space for which the above equation and the following conditions hold:1.   c  ∈  N2.   0  ≤  x  ,  y  ≤  1I.E, which constraints/inequalities   x &amp;amp;   y must fulfill (in terms of   c)

Aibling6n2re · Accepted Answer

As it is pointed out in OP, the inequalities (1),(2) can be written in one as  c  ≤            c      2        (          x      2        +          y      2        )    +    2    c    (    x    +    y    )    +    2    +      1    2    &amp;lt;  c  +  1or  c  −      1    2    ≤            c      2        (          x      2        +          y      2        )    +    2    c    (    x    +    y    )    +    2    &amp;lt;  c  +      1    2  Since   c is a positive integer, the last double inequality is equivalent to            (      c      −              1        2            )        2    ≤      (    c    x    +    1          )      2        +    (    c    y    +    1          )      2        &amp;lt;            (      c      +              1        2            )        2  and further to

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