x^(3/2)-40x^(1/2)=0

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Solution for x^(3/2)-40x^(1/2)=0 equation: 


D( x )

x < 0

x < 0

x in <0:+oo)

x^(3/2)-(40*x^(1/2)) = 0

x^(3/2)-40*x^(1/2) = 0

t_1 = x^(1/2)

1*t_1^3-40*t_1^1 = 0

t_1^3-40*t_1 = 0

t_1*(t_1^2-40) = 0

1*t_1^2 = 40 // : 1

t_1^2 = 40

t_1^2 = 40 // ^ 1/2

abs(t_1) = 2*10^(1/2)

t_1 = 2*10^(1/2) or t_1 = -(2*10^(1/2))

t_1 = 0

t_1 = 0

t_1 = 2*10^(1/2)

x^(1/2)-(2*10^(1/2)) = 0

x^(1/2)-2*10^(1/2) = 0

1*x^(1/2) = -(-2*10^(1/2)) // : 1

x^(1/2) = 2*10^(1/2)

x^(1/2) = 2*10^(1/2) // ^ 2

x = 40

t_1 = -(2*10^(1/2))

x^(1/2)+2*10^(1/2) = 0

1*x^(1/2) = -(2*10^(1/2)) // : 1

x^(1/2) = -2*10^(1/2)

( -2*10^(1/2) < 0 i 1/2 in (0:1) ) => x należy do O

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 { 40, 0 }

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