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1. Let x and y be real numbers such that x^2 + y^2 = 4(x + y). Find the largest possible value of x.

 

2. The lines y = x/3 and y = 13x/9 are drawn in the coordinate plane. Find the slope of the line that bisects the angle between these lines.

 Jun 1, 2020
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1. The maximum value of x is 5 + sqrt(3).

 

2. Using the angle bisector theorem, I found that the slope of the line in the middle is 7/5.

 Jun 1, 2020

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