5x^(-3/4)+10x^(1/4)

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Solution for 5x^(-3/4)+10x^(1/4) equation: 


D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

10*x^(1/4)+5*x^(-3/4) = 0

t_1 = x^(1/4)

10*t_1^1+5*t_1^-3 = 0

10*t_1+5*t_1^-3 = 0

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

1*t_1^-4 = -2 // : 1

t_1^-4 = -2

-4 < 0

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

1 = -2*t_1^4 // : -2

-1/2 = t_1^4

5*t_1 = 0

5*t_1 = 0 // : 5

t_1 = 0

t_1 = 0

x^(1/4)+0 = 0

x^(1/4) = 0

1*x^(1/4) = 0 // : 1

x^(1/4) = 0

x = 0

x in { 0} 

x belongs to the empty set

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