This is quartic and we can convert to sum of quartic of the form (a+x)^4 + (a-x)^4 by choosing x and 2-x equdistance from mean that is 1
let x = 1- t
then 2 - x = t+ 1
x^4 + (2-x)^2 = (1-t)^4 + (1+t)^4 = 2(t^4 + 6t^2+ 1)
hence 2(t^4 + 6t^2+ 1) = 34 or t^ 4 + 6t^2 - 16 =0
let x = 1- t
then 2 - x = t+ 1
x^4 + (2-x)^2 = (1-t)^4 + (1+t)^4 = 2(t^4 + 6t^2+ 1)
hence 2(t^4 + 6t^2+ 1) = 34 or t^ 4 + 6t^2 - 16 =0
or (t^2-2)(t^2-8) = 0
t = sqrt(2) or - sqrt(2) or 2 sqrt(2)i or -2(sqrt(2) i
hence x= 1 + sqrt(2) or 1- sqrt(2) or 1 + 2 sqrt(2) i or 1- 2sqrt(2) i
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