4x^(-5/2)+8x^(1/2)

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Solution for 4x^(-5/2)+8x^(1/2) equation: 


D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

8*x^(1/2)+4*x^(-5/2) = 0

t_1 = x^(1/2)

8*t_1^1+4*t_1^-5 = 0

8*t_1+4*t_1^-5 = 0

4*t_1*(t_1^-6+2) = 0

1*t_1^-6 = -2 // : 1

t_1^-6 = -2

-6 < 0

1/(t_1^6) = -2 // * t_1^6

1 = -2*t_1^6 // : -2

-1/2 = t_1^6

4*t_1 = 0

4*t_1 = 0 // : 4

t_1 = 0

t_1 = 0

x^(1/2)+0 = 0

x^(1/2) = 0

1*x^(1/2) = 0 // : 1

x^(1/2) = 0

x = 0

x in { 0} 

x belongs to the empty set

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