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Let a and b be real numbers such that a + b = 4 and a^4 + b^4 = 16.

(a) Find all possible values of ab
(b) Find all possible values of a + b
(c) Find all possible values of a and b

 Dec 4, 2022
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It is easy to show  x^4+y^4=16  is contained in the circle  x^2+y^2=4*sqrt(2). But x+y=4 is tangent to the circle  x^2+y^2=8 . Since 8 > 4*sqrt(2) , then there is no intersection.


Conclusion: There is no "real solution" to your question, only "imaginary solution"!

 Dec 4, 2022

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