(x*x)-10/(x*x)=3

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Solution for (x*x)-10/(x*x)=3 equation: 


D( x )

x*x = 0

x*x = 0

x*x = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

x*x-(10/(x*x)) = 3 // - 3

x*x-(10/(x*x))-3 = 0

x*x-10*x^-2-3 = 0

x^2-10*x^-2-3 = 0

t_1 = x^2

1*t_1^1-10*t_1^-1-3 = 0

1*t_1^1-10*t_1^-1-3*t_1^0 = 0

(1*t_1^2-3*t_1^1-10*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-3*t_1^1-10*t_1^0) = 0

t_1^1

t_1^2-3*t_1-10 = 0

t_1^2-3*t_1-10 = 0

DELTA = (-3)^2-(-10*1*4)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+3)/(1*2) or t_1 = (3-49^(1/2))/(1*2)

t_1 = 5 or t_1 = -2

t_1 in { -2, 5} 

t_1 = -2

x^2+2 = 0

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

x^2 = -2

t_1 = 5

x^2-5 = 0

1*x^2 = 5 // : 1

x^2 = 5

x^2 = 5 // ^ 1/2

abs(x) = 5^(1/2)

x = 5^(1/2) or x = -5^(1/2)

x in { 5^(1/2), -5^(1/2) }

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