x^(3/2)-25x^(-1/2)

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Solution for x^(3/2)-25x^(-1/2) equation: 


D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

x^(3/2)-(25*x^(-1/2)) = 0

x^(3/2)-25*x^(-1/2) = 0

t_1 = x^(1/2)

1*t_1^3-25*t_1^-1 = 0

t_1^3-25*t_1^-1 = 0

t_1^-1*(t_1^4-25) = 0

1*t_1^4 = 25 // : 1

t_1^4 = 25

t_1^4 = 25 // ^ 1/4

abs(t_1) = 25^(1/4)

t_1 = 25^(1/4) or t_1 = -25^(1/4)

1/t_1 = 0

1*t_1^-1 = 0 // : 1

t_1^-1 = 0

t_1 naleu017Cy do O

t_1 = 25^(1/4)

x^(1/2)-25^(1/4) = 0

1*x^(1/2) = 25^(1/4) // : 1

x^(1/2) = 25^(1/4)

x^(1/2) = 25^(1/4) // ^ 2

x = 5

t_1 = -25^(1/4)

x^(1/2)+25^(1/4) = 0

1*x^(1/2) = -25^(1/4) // : 1

x^(1/2) = -25^(1/4)

( -25^(1/4) < 0 i 1/2 in (0:1) ) => x naleu017Cy do O

x = 5

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