x^2=1/x^2

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Solution for x^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)

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

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

x^2-x^-2 = 0

t_1 = x^2

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

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

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

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

t_1^1

t_1^2-1 = 0

t_1^2-1 = 0

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

DELTA = 4

DELTA > 0

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

t_1 = 1 or t_1 = -1

t_1 in { -1, 1} 

t_1 = -1

x^2+1 = 0

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

x^2 = -1

t_1 = 1

x^2-1 = 0

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

x in { 1, -1 }

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