Within the boundaries
Find the number of integer solutions of the pairs such that is fulfilled.
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1 solution
Moderator note:
I've edited your problem statement explaining that we're looking for integer solutions only.
Your phrasing is poorly written. You did not explain any relevant step in your working. Why do we start with ? What does it mean? And why is not possible? Why the sudden restriction? What exactly are you trying to do?
There's a much simpler solution: Draw a circle of radius 5 on a Cartesian Plane that is inscribed inside a square of side length 10. This time, find the number of lattice points (integer coordinates) that falls outside of the circle but inside the square. What does this value mean?
Unless you're familiar with Gauss Circle Problem then the answer is immediate.
-4,-3,-2,-1,0,1,2,3,4 So, nine values are possible so 9X9=81 values are possible but all the combinations of 3,-3,4,-4 are not possible .
There are 12 such ordered pairs. So, 81-12=69
And, hence; 69 is the correct answer.