x^4-(25+1/25)x^2+1=0

Solution for x^4-(25+1/25)x^2+1=0 equation:

x in (-oo:+oo)

x^4-((1/25+25)*x^2)+1 = 0

x^4-626/25*x^2+1 = 0

t_1 = x^2

1*t_1^2-626/25*t_1^1+1 = 0

t_1^2-626/25*t_1+1 = 0

DELTA = (-626/25)^2-(1*1*4)

DELTA = 389376/625

DELTA > 0

t_1 = ((389376/625)^(1/2)+626/25)/(1*2) or t_1 = (626/25-(389376/625)^(1/2))/(1*2)

t_1 = 25 or t_1 = 1/25

t_1 = 1/25

x^2-1/25 = 0

1*x^2 = 1/25 // : 1

x^2 = 1/25

x^2 = 1/25 // ^ 1/2

abs(x) = 1/5

x = 1/5 or x = -1/5

t_1 = 25

x^2-25 = 0

1*x^2 = 25 // : 1

x^2 = 25

x^2 = 25 // ^ 1/2

abs(x) = 5

x = 5 or x = -5

x in { 1/5, -1/5, 5, -5 }