Question 197967
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (n - 5)^2 = 20]


Take the square root of both sides, considering both the positive and negative square roots:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n - 5 = \pm \sqrt{20}]


Solve for the variable:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n = 5 \pm \sqrt{20}]


Find the prime factorization of the radicand:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 20 = 2\cdot2\cdot5]


There are two factors of 2 in the radicand.  Eliminate them and take one of them outside:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{20} = \sqrt{4\cdot5} = 2\sqrt{5}]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n = 5 \pm 2\sqrt{5}]


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