4x^2-1/x^2

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Solution for 4x^2-1/x^2 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

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

4*x^2-x^-2 = 0

t_1 = x^2

4*t_1^1-1*t_1^-1 = 0

4*t_1^1-1*t_1^-1 = 0

(4*t_1^2-1*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(4*t_1^2-1*t_1^0) = 0

t_1^1

4*t_1^2-1 = 0

4*t_1^2-1 = 0

DELTA = 0^2-(-1*4*4)

DELTA = 16

DELTA > 0

t_1 = (16^(1/2)+0)/(2*4) or t_1 = (0-16^(1/2))/(2*4)

t_1 = 1/2 or t_1 = -1/2

t_1 in { -1/2, 1/2} 

t_1 = -1/2

x^2+1/2 = 0

1*x^2 = -1/2 // : 1

x^2 = -1/2

t_1 = 1/2

x^2-1/2 = 0

1*x^2 = 1/2 // : 1

x^2 = 1/2

x^2 = 1/2 // ^ 1/2

abs(x) = (1/2)^(1/2)

x = (1/2)^(1/2) or x = -(1/2)^(1/2)

x in { (1/2)^(1/2), -(1/2)^(1/2) }

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