x-12=16x^(1/2)

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Solution for x-12=16x^(1/2) equation:


D( x )

x < 0

x < 0

x in <0:+oo)

x-12 = 16*x^(1/2) // - 16*x^(1/2)

x-(16*x^(1/2))-12 = 0

x-16*x^(1/2)-12 = 0

t_1 = x^(1/2)

1*t_1^2-16*t_1^1-12 = 0

t_1^2-16*t_1-12 = 0

DELTA = (-16)^2-(-12*1*4)

DELTA = 304

DELTA > 0

t_1 = (304^(1/2)+16)/(1*2) or t_1 = (16-304^(1/2))/(1*2)

t_1 = (4*19^(1/2)+16)/2 or t_1 = (16-4*19^(1/2))/2

t_1 = (16-4*19^(1/2))/2

x^(1/2)-((16-4*19^(1/2))/2) = 0

1*x^(1/2) = (16-4*19^(1/2))/2 // : 1

x^(1/2) = (16-4*19^(1/2))/2

( (16-4*19^(1/2))/2 < 0 i 1/2 in (0:1) ) => x należy do O

t_1 = (4*19^(1/2)+16)/2

x^(1/2)-((4*19^(1/2)+16)/2) = 0

1*x^(1/2) = (4*19^(1/2)+16)/2 // : 1

x^(1/2) = (4*19^(1/2)+16)/2

x^(1/2) = (4*19^(1/2)+16)/2 // ^ 2

x = ((4*19^(1/2)+16)^2)/4

x = ((4*19^(1/2)+16)^2)/4

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