2x^(1/2)-x^(1/4)-3=0

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Solution for 2x^(1/2)-x^(1/4)-3=0 equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

2*x^(1/2)-x^(1/4)-3 = 0

t_1 = x^(1/4)

2*t_1^2-1*t_1^1-3 = 0

2*t_1^2-t_1-3 = 0

DELTA = (-1)^2-(-3*2*4)

DELTA = 25

DELTA > 0

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

t_1 = 3/2 or t_1 = -1

t_1 = -1

x^(1/4)+1 = 0

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

x^(1/4) = -1

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

t_1 = 3/2

x^(1/4)-3/2 = 0

1*x^(1/4) = 3/2 // : 1

x^(1/4) = 3/2

x^(1/4) = 3/2 // ^ 4

x = 81/16

x = 81/16

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