Question 484360
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{y\ +\ 10}\ =\ y\ -\ 2]


Square both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ +\ 10\ =\ y^2\ -\ 4y\ +\ 4]


Collect like terms:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y^2\ -\ 5y\ -\ 6\ =\ 0]


Factor:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (y\ -\ 6)(y\ +\ 1)\ =\ 0]


Hence, *[tex \Large y\ =\ 6] or *[tex \Large y\ =\ -1]


But you have to check both potential solutions in the original equation.  Discard any or all solutions that do not result in a true statement when substituted into the original equation.  Hint:  *[tex \Large \sqrt{x}] represents the POSITIVE square root ONLY.


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