Question 376685
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Let *[tex \Large x] represent one of the numbers and *[tex \Large y] represent the other.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ y\ = 6]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{x}\ -\ \sqrt{y}\ =\ 1]


Separate the radicals:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{x}\ =\ \sqrt{y}\ +\ 1]


Square both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ y\ +\ 2\sqrt{y}\ +\ 1]


Add *[tex \Large -y\ -\ 1] to both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ y\ -\ 1\ =\ 2\sqrt{y}]


Substitute:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6\ -\ 1\ =\ 2\sqrt{y}]


Square both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 25\ =\ 4y]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ 6.25]


And therefore


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 12.25]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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