Question 255920
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Let *[tex \Large x] represent the larger of the two numbers.


Let *[tex \Large y] represent the smaller of the two numbers.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ y\ =\ 5]


Therefore:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ x\ -\ 5]


But


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ + y^2\ = 233]


Therefore, by substitution:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ + \left(x\,-\,5\right)^2\ = 233]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ x^2\ -\ 10x\ +\ 25\ = 233]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 5x\ -\ 104\ =\ 0]


Solve the quadratic and discard the negative root.  The larger number is the positive root.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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