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

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


D( x )

2*x < 0

x < 0

2*x < 0

2*x < 0

2*x+0 < 0 // - 0

2*x < 0 // : 2

x < 0/2

x < 0

x < 0

x in <0:+oo)

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

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

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

t_1 = x^(1/4)

2^(1/2)*t_1^2-7*t_1^1+4 = 0

2^(1/2)*t_1^2-7*t_1+4 = 0

DELTA = (-7)^2-(4*4*2^(1/2))

DELTA = 49-16*2^(1/2)

DELTA = 26.37258304

DELTA > 0

t_1 = ((49-16*2^(1/2))^(1/2)+7)/(2*2^(1/2)) or t_1 = (7-(49-16*2^(1/2))^(1/2))/(2*2^(1/2))

t_1 = (7-(49-16*2^(1/2))^(1/2))/(2*2^(1/2))

x^(1/4)-((7-(49-16*2^(1/2))^(1/2))/(2*2^(1/2))) = 0

1*x^(1/4) = (7-(49-16*2^(1/2))^(1/2))/(2*2^(1/2)) // : 1

x^(1/4) = (7-(49-16*2^(1/2))^(1/2))/(2*2^(1/2))

x^(1/4) = (7-(49-16*2^(1/2))^(1/2))/(2*2^(1/2)) // ^ 4

x = ((7-(49-16*2^(1/2))^(1/2))^4)/64

t_1 = ((49-16*2^(1/2))^(1/2)+7)/(2*2^(1/2))

x^(1/4)-(((49-16*2^(1/2))^(1/2)+7)/(2*2^(1/2))) = 0

1*x^(1/4) = ((49-16*2^(1/2))^(1/2)+7)/(2*2^(1/2)) // : 1

x^(1/4) = ((49-16*2^(1/2))^(1/2)+7)/(2*2^(1/2))

x^(1/4) = ((49-16*2^(1/2))^(1/2)+7)/(2*2^(1/2)) // ^ 4

x = (((49-16*2^(1/2))^(1/2)+7)^4)/64

x in { ((7-(49-16*2^(1/2))^(1/2))^4)/64, (((49-16*2^(1/2))^(1/2)+7)^4)/64 }

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