Question 629009
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ \sqrt{2x\ +\ 21}\ -\ \sqrt{2x}\ -\ 3]


Set the function equal to zero since zero is the value of the function at the *[tex \LARGE x] intercept(s).  Solve for *[tex \LARGE x]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0\ =\ \sqrt{2x\ +\ 21}\ -\ \sqrt{2x}\ -\ 3]


Add *[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{2x}\ -\ 3] to both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{2x\ +\ 21}\ =\ \sqrt{2x}\ -\ 3]


Square both sides


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\ +\ 21\ =\ 2x\ -\ 6\sqrt{2x}\ +\ 9]


Collect like terms


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6\sqrt{2x}\ =\ -12]


Multiply by *[tex \LARGE \frac{1}{6}]


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


Square both sides


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\ =\ 4]


Solve for *[tex \LARGE x], then check your answer by substitution into the original equation.


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