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# help algebra

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Find the largest value of x for which
x^2 + y^2 = x + y + 4
has a solution, if x and y are real.

Apr 16, 2022

#1
+9461
+1

We visualize the equation as a circle on the coordinate plane.

The circle is centered at $$\left(\dfrac12, \dfrac12\right)$$ and has a radius $$\dfrac{3\sqrt 2}2$$. Therefore, for the largest value of x, we find the maximum possible x-coordinate on the circle, i.e., the x-coordinate of the right-most point.

$$\max x = \dfrac12 + \text{radius of circle} = \dfrac{1 + 3\sqrt 2}2$$

Further explanations are typed in the graph.

Apr 16, 2022

#1
+9461
+1

We visualize the equation as a circle on the coordinate plane.

The circle is centered at $$\left(\dfrac12, \dfrac12\right)$$ and has a radius $$\dfrac{3\sqrt 2}2$$. Therefore, for the largest value of x, we find the maximum possible x-coordinate on the circle, i.e., the x-coordinate of the right-most point.

$$\max x = \dfrac12 + \text{radius of circle} = \dfrac{1 + 3\sqrt 2}2$$

Further explanations are typed in the graph.

MaxWong Apr 16, 2022