Question 372253
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We know the two points are of the form *[tex \Large (0,\beta_1)] and *[tex \Large (0,\beta_2)]


Using the distance formula:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ sqrt{(x_1\ -\ x_2)^2\ +\ (y_1\ -\ y_2)^2}]


Where one of the points is *[tex \Large (4,2)], the other point is *[tex \Large (0,\beta_i)], and the distance is 5, we can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 16\ +\ (2\ -\ \beta_i)^2\ =\ 25]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (2\ -\ \beta_i)^2\ =\ 9]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\ -\ \beta_i\ =\ \pm3]


Hence


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \beta_1\ =\ -1]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \beta_2\ =\ 5]


Making the two points *[tex \Large (0,-1)] and *[tex \Large (0,5)]


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