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

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


D( x )

2*x < 0

2*x < 0

2*x < 0

2*x+0 < 0 // - 0

2*x < 0 // : 2

x < 0/2

x < 0

x in <0:+oo)

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

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

t_1 = x^(1/2)

1*t_1^2-1*t_1^1-4 = 0

t_1^2-t_1-4 = 0

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

DELTA = 17

DELTA > 0

t_1 = (17^(1/2)+1)/(1*2) or t_1 = (1-17^(1/2))/(1*2)

t_1 = (17^(1/2)+1)/2 or t_1 = (1-17^(1/2))/2

t_1 = (1-17^(1/2))/2

x^(1/2)-((1-17^(1/2))/2) = 0

1*x^(1/2) = (1-17^(1/2))/2 // : 1

x^(1/2) = (1-17^(1/2))/2

( (1-17^(1/2))/2 < 0 i 1/2 in (0:1) ) => x należy do O

t_1 = (17^(1/2)+1)/2

x^(1/2)-((17^(1/2)+1)/2) = 0

1*x^(1/2) = (17^(1/2)+1)/2 // : 1

x^(1/2) = (17^(1/2)+1)/2

x^(1/2) = (17^(1/2)+1)/2 // ^ 2

x = ((17^(1/2)+1)^2)/4

x = ((17^(1/2)+1)^2)/4

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