2x^(1/2)-7x^(1/4)+2=0

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Solution for 2x^(1/2)-7x^(1/4)+2=0 equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

2*x^(1/2)-(7*x^(1/4))+2 = 0

2*x^(1/2)-7*x^(1/4)+2 = 0

t_1 = x^(1/4)

2*t_1^2-7*t_1^1+2 = 0

2*t_1^2-7*t_1+2 = 0

DELTA = (-7)^2-(2*2*4)

DELTA = 33

DELTA > 0

t_1 = (33^(1/2)+7)/(2*2) or t_1 = (7-33^(1/2))/(2*2)

t_1 = (33^(1/2)+7)/4 or t_1 = (7-33^(1/2))/4

t_1 = (7-33^(1/2))/4

x^(1/4)-((7-33^(1/2))/4) = 0

1*x^(1/4) = (7-33^(1/2))/4 // : 1

x^(1/4) = (7-33^(1/2))/4

x^(1/4) = (7-33^(1/2))/4 // ^ 4

x = ((7-33^(1/2))^4)/256

t_1 = (33^(1/2)+7)/4

x^(1/4)-((33^(1/2)+7)/4) = 0

1*x^(1/4) = (33^(1/2)+7)/4 // : 1

x^(1/4) = (33^(1/2)+7)/4

x^(1/4) = (33^(1/2)+7)/4 // ^ 4

x = ((33^(1/2)+7)^4)/256

x in { ((7-33^(1/2))^4)/256, ((33^(1/2)+7)^4)/256 }

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