(X^4+2x^2-x+5)/(x^2-x+1)

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Solution for (X^4+2x^2-x+5)/(x^2-x+1) equation: 


D( x )

x^2-x+1 = 0

x^2-x+1 = 0

x^2-x+1 = 0

x^2-x+1 = 0

DELTA = (-1)^2-(1*1*4)

DELTA = -3

DELTA < 0

x in (-oo:+oo)

t_1 = X^4+5

t_1+2*x^2-x = 0

t_1+2*x^2-x = 0

DELTA = (-1)^2-(2*4*t_1)

DELTA = 1-8*t_1

1-8*t_1 = 0

1-8*t_1 = 0 // - 1

-8*t_1 = -1 // : -8

t_1 = -1/(-8)

t_1 = 1/8

DELTA = 0  <=>  t_2 = 1/8

x = 1/(2*2) i t_1 = 1/8

x = 1/4 i t_1 = 1/8

( x = ((1-8*t_1)^(1/2)+1)/(2*2) or x = (1-(1-8*t_1)^(1/2))/(2*2) ) i t_1 > 1/8

( x = ((1-8*t_1)^(1/2)+1)/4 or x = (1-(1-8*t_1)^(1/2))/4 ) i t_1 > 1/8

t_1-1/8 > 0

t_1-1/8 > 0 // + 1/8

t_1 > 1/8

x in { 1/4, ((1-8*(X^4+5))^(1/2)+1)/4, (1-(1-8*(X^4+5))^(1/2))/4 }

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