100x^-4/3-409x^-2/3+36=0

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Solution for 100x^-4/3-409x^-2/3+36=0 equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

(100*x^-4)/3-((409*x^-2)/3)+36 = 0

(-409/3)*x^-2+(100*x^-4)/3+36 = 0

100/3*x^-4-409/3*x^-2+36 = 0

t_1 = x^-2

100/3*t_1^2-409/3*t_1^1+36 = 0

100/3*t_1^2-409/3*t_1+36 = 0

DELTA = (-409/3)^2-(4*100/3*36)

DELTA = 124081/9

DELTA > 0

t_1 = ((124081/9)^(1/2)+409/3)/(2*100/3) or t_1 = (409/3-(124081/9)^(1/2))/(2*100/3)

t_1 = 3/200*((124081/9)^(1/2)+409/3) or t_1 = 3/200*(409/3-(124081/9)^(1/2))

t_1 = 3/200*(409/3-(124081/9)^(1/2))

x^-2-(3/200*(409/3-(124081/9)^(1/2))) = 0

x^-2-3/200*(409/3-(124081/9)^(1/2)) = 0

1*x^-2 = -(-3/200*(409/3-(124081/9)^(1/2))) // : 1

x^-2 = 3/200*(409/3-(124081/9)^(1/2))

-2 < 0

1/(x^2) = 3/200*(409/3-(124081/9)^(1/2)) // * x^2

1 = 3/200*(409/3-(124081/9)^(1/2))*x^2 // : 3/200*(409/3-(124081/9)^(1/2))

200/3*(409/3-(124081/9)^(1/2))^-1 = x^2

x^2 = 200/3*(409/3-(124081/9)^(1/2))^-1 // ^ 1/2

abs(x) = (200/3)^(1/2)*(409/3-(124081/9)^(1/2))^(-1/2)

x = (200/3)^(1/2)*(409/3-(124081/9)^(1/2))^(-1/2) or x = -((200/3)^(1/2)*(409/3-(124081/9)^(1/2))^(-1/2))

t_1 = 3/200*((124081/9)^(1/2)+409/3)

x^-2-(3/200*((124081/9)^(1/2)+409/3)) = 0

x^-2-3/200*((124081/9)^(1/2)+409/3) = 0

1*x^-2 = -(-3/200*((124081/9)^(1/2)+409/3)) // : 1

x^-2 = 3/200*((124081/9)^(1/2)+409/3)

-2 < 0

1/(x^2) = 3/200*((124081/9)^(1/2)+409/3) // * x^2

1 = 3/200*((124081/9)^(1/2)+409/3)*x^2 // : 3/200*((124081/9)^(1/2)+409/3)

200/3*((124081/9)^(1/2)+409/3)^-1 = x^2

x^2 = 200/3*((124081/9)^(1/2)+409/3)^-1 // ^ 1/2

abs(x) = (200/3)^(1/2)*((124081/9)^(1/2)+409/3)^(-1/2)

x = (200/3)^(1/2)*((124081/9)^(1/2)+409/3)^(-1/2) or x = -((200/3)^(1/2)*((124081/9)^(1/2)+409/3)^(-1/2))

x in { (200/3)^(1/2)*(409/3-(124081/9)^(1/2))^(-1/2), -((200/3)^(1/2)*(409/3-(124081/9)^(1/2))^(-1/2)), (200/3)^(1/2)*((124081/9)^(1/2)+409/3)^(-1/2), -((200/3)^(1/2)*((124081/9)^(1/2)+409/3)^(-1/2)) }

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