x^2-3=4/x^2

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Solution for x^2-3=4/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^2-3 = 4/(x^2) // - 4/(x^2)

x^2-(4/(x^2))-3 = 0

x^2-4*x^-2-3 = 0

t_1 = x^2

1*t_1^1-4*t_1^-1-3 = 0

1*t_1^1-4*t_1^-1-3*t_1^0 = 0

(1*t_1^2-3*t_1^1-4*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-3*t_1^1-4*t_1^0) = 0

t_1^1

t_1^2-3*t_1-4 = 0

t_1^2-3*t_1-4 = 0

DELTA = (-3)^2-(-4*1*4)

DELTA = 25

DELTA > 0

t_1 = (25^(1/2)+3)/(1*2) or t_1 = (3-25^(1/2))/(1*2)

t_1 = 4 or t_1 = -1

t_1 in { -1, 4} 

t_1 = -1

x^2+1 = 0

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

x^2 = -1

t_1 = 4

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in { 2, -2 }

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