Question 696766
x1=(-p-sqrt(p^2-4*q))/2
x2=(-p+sqrt(p^2-4*q))/2

solve
q^4+q*(2*q-p^2)+1=0

p=(q^2 + 1)/q^(1/2)
OR
p= -(q^2 + 1)/q^(1/2)

sub p=(q^2 + 1)/q^(1/2) in x1 and x2 you  get:

x1 =
 
- ((q^2 + 1)^2/q - 4*q)^(1/2)/2 - (q^2 + 1)/(2*q^(1/2))
 
 
x2 =
 
((q^2 + 1)^2/q - 4*q)^(1/2)/2 - (q^2 + 1)/(2*q^(1/2))

sub x1  in

x^2+p*x+q

it is =0 

sub x2  in

x^2+p*x+q

it is =0

then q^4+q*(2*q-p^2)+1=0

you get the same result when use:
p= -(q^2 + 1)/q^(1/2)