Question 191206
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \sqrt{2d - 3}\ =\ d - 9]


Square both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  2d - 3\ =\ d^2 - 18d + 81]


Collect terms and put the equation in standard quadratic form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  d^2 - 20d + 84 = 0]


Factor:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  (d - 6)(d -14) = 0]


Hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  d = 6]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  d = 14]


Check the answers:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \sqrt{2(14) - 3}\ =^{\tiny{?}}\ 14 - 9]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \sqrt{25}\ =\ 5]


14 checks


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \sqrt{2(6) - 3}\ =^{\tiny{?}}\ 6 - 9]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \sqrt{9}\ =\ 3 \neq -3]


6 is an extraneous root introduced by the operation of squaring the variable.  Exclude this root.


Your answer is 14 only.


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