2x^(1/2)-5x^(1/4)-3=0

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Solution for 2x^(1/2)-5x^(1/4)-3=0 equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

2*x^(1/2)-(5*x^(1/4))-3 = 0

2*x^(1/2)-5*x^(1/4)-3 = 0

t_1 = x^(1/4)

2*t_1^2-5*t_1^1-3 = 0

2*t_1^2-5*t_1-3 = 0

DELTA = (-5)^2-(-3*2*4)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+5)/(2*2) or t_1 = (5-49^(1/2))/(2*2)

t_1 = 3 or t_1 = -1/2

t_1 = -1/2

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

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

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

( -1/2 < 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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