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
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"!