x^2-(-15/x)^2=16

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Solution for x^2-(-15/x)^2=16 equation: 


D( x )

x = 0

x = 0

x = 0

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

x^2-(-15/x)^2 = 16 // - 16

x^2-(-15/x)^2-16 = 0

x^2-225*x^-2-16 = 0

t_1 = x^2

1*t_1^1-225*t_1^-1-16 = 0

1*t_1^1-225*t_1^-1-16*t_1^0 = 0

(1*t_1^2-16*t_1^1-225*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-16*t_1^1-225*t_1^0) = 0

t_1^1

t_1^2-16*t_1-225 = 0

t_1^2-16*t_1-225 = 0

DELTA = (-16)^2-(-225*1*4)

DELTA = 1156

DELTA > 0

t_1 = (1156^(1/2)+16)/(1*2) or t_1 = (16-1156^(1/2))/(1*2)

t_1 = 25 or t_1 = -9

t_1 in { -9, 25} 

t_1 = -9

x^2+9 = 0

1*x^2 = -9 // : 1

x^2 = -9

t_1 = 25

x^2-25 = 0

1*x^2 = 25 // : 1

x^2 = 25

x^2 = 25 // ^ 1/2

abs(x) = 5

x = 5 or x = -5

x in { 5, -5 }

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