x^(2/5)+x^(1/5)+1=6

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Solution for x^(2/5)+x^(1/5)+1=6 equation: 


x in (-oo:+oo)

x^(2/5)+x^(1/5)+1 = 6 // - 6

x^(2/5)+x^(1/5)-6+1 = 0

x^(2/5)+x^(1/5)-5 = 0

t_1 = x^(1/5)

1*t_1^2+1*t_1^1-5 = 0

t_1^2+t_1-5 = 0

DELTA = 1^2-(-5*1*4)

DELTA = 21

DELTA > 0

t_1 = (21^(1/2)-1)/(1*2) or t_1 = (-21^(1/2)-1)/(1*2)

t_1 = (21^(1/2)-1)/2 or t_1 = (-(21^(1/2)+1))/2

t_1 = (-(21^(1/2)+1))/2

x^(1/5)-((-(21^(1/2)+1))/2) = 0

x^(1/5)+(1/2)*(21^(1/2)+1) = 0

1*x^(1/5) = -(1/2*(21^(1/2)+1)) // : 1

x^(1/5) = -1/2*(21^(1/2)+1)

( -1/2*(21^(1/2)+1) < 0 i 1/5 in (0:1) ) => x naleu017Cy do O

t_1 = (21^(1/2)-1)/2

x^(1/5)-((21^(1/2)-1)/2) = 0

1*x^(1/5) = (21^(1/2)-1)/2 // : 1

x^(1/5) = (21^(1/2)-1)/2

x^(1/5) = (21^(1/2)-1)/2 // ^ 5

x = ((21^(1/2)-1)^5)/32

x = ((21^(1/2)-1)^5)/32

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