x^(1/2)-6=x^(1/4)

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Solution for x^(1/2)-6=x^(1/4) equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

x^(1/2)-6 = x^(1/4) // - x^(1/4)

x^(1/2)-x^(1/4)-6 = 0

t_1 = x^(1/4)

1*t_1^2-1*t_1^1-6 = 0

t_1^2-t_1-6 = 0

DELTA = (-1)^2-(-6*1*4)

DELTA = 25

DELTA > 0

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

t_1 = 3 or t_1 = -2

t_1 = -2

x^(1/4)+2 = 0

1*x^(1/4) = -2 // : 1

x^(1/4) = -2

( -2 < 0 i 1/4 in (0:1) ) => x należy do O

t_1 = 3

x^(1/4)-3 = 0

1*x^(1/4) = 3 // : 1

x^(1/4) = 3

x^(1/4) = 3 // ^ 4

x = 81

x = 81

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