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Grades 11-12 Video Solutions 2013
Levels 11&12 Video Solutions 2013 problem24
Levels 11&12 Video Solutions 2013 problem24
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Video Summary
The given equation \(x^2 + y^2 = |x| + |y|\) can be analyzed by considering different quadrants. By examining only the first quadrant, where \(x\) and \(y\) are non-negative, the equation simplifies to \(x^2 + y^2 = x + y\). Completing the square transforms it into \((x - \frac{1}{2})^2 + (y - \frac{1}{2})^2 = \frac{1}{2}\), representing a circle with center \((\frac{1}{2}, \frac{1}{2})\) and radius \(\sqrt{\frac{1}{2}}\). Thus, the equation has infinitely many solutions, corresponding to points on the circle.
Keywords
equation
quadrants
circle
solutions
radius
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