Question 194754
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \  (x + 4)^4 - (x + 4)^2 - 6 = 0]


Let *[tex \LARGE u = (x + 4)^2]


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


Factor:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (u - 3)(u - 2) = 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ u - 3 = 0 \ \ \Rightarrow\ \ u = 3] or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ u - 2 = 0 \ \ \Rightarrow\ \ u = 2]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (x + 4)^2 = 3 \ \ \Rightarrow\ \ x^2 + 8x + 13 = 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_{1,2} = \frac{-8 \pm sqrt{64 - 52}}{2} = -4 \pm \sqrt{3}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (x + 4)^2 = 2 \ \ \Rightarrow\ \ x^2 + 8x + 14 = 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_{3,4} = \frac{-8 \pm sqrt{64 - 56}}{2} = -4 \pm \sqrt{2}]



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