2021 April MIMC 10 Problems/Problem 18
What can be a description of the set of solutions for this: ?
Two overlapping circles with each area .
Four not overlapping circles with each area .
There are two overlapping circles on the right of the -axis with each area and the intersection area of two overlapping circles on the left of the -axis with each area .
Four overlapping circles with each area .
There are two overlapping circles on the right of the -axis with each area and the intersection area of two overlapping circles on the left of the -axis with each area .
Solution
First, we want to graph this equation. use the technique of absolute value, there will be four cases of . The four cases are all circles with radius of . However, we realize that does not have an absolute value sign, so the left side is different from the right. Therefore, our answer would be .