x^2-(4/x)^2=60

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Solution for x^2-(4/x)^2=60 equation: 


D( x )

x = 0

x = 0

x = 0

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

x^2-(4/x)^2 = 60 // - 60

x^2-(4/x)^2-60 = 0

x^2-16*x^-2-60 = 0

t_1 = x^2

1*t_1^1-16*t_1^-1-60 = 0

1*t_1^1-16*t_1^-1-60*t_1^0 = 0

(1*t_1^2-60*t_1^1-16*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-60*t_1^1-16*t_1^0) = 0

t_1^1

t_1^2-60*t_1-16 = 0

t_1^2-60*t_1-16 = 0

DELTA = (-60)^2-(-16*1*4)

DELTA = 3664

DELTA > 0

t_1 = (3664^(1/2)+60)/(1*2) or t_1 = (60-3664^(1/2))/(1*2)

t_1 = (4*229^(1/2)+60)/2 or t_1 = (60-4*229^(1/2))/2

t_1 in { (60-4*229^(1/2))/2, (4*229^(1/2)+60)/2} 

t_1 = (60-4*229^(1/2))/2

x^2-((60-4*229^(1/2))/2) = 0

1*x^2 = (60-4*229^(1/2))/2 // : 1

x^2 = (60-4*229^(1/2))/2

t_1 = (4*229^(1/2)+60)/2

x^2-((4*229^(1/2)+60)/2) = 0

1*x^2 = (4*229^(1/2)+60)/2 // : 1

x^2 = (4*229^(1/2)+60)/2

x^2 = (4*229^(1/2)+60)/2 // ^ 1/2

abs(x) = ((4*229^(1/2)+60)^(1/2))/(2^(1/2))

x = ((4*229^(1/2)+60)^(1/2))/(2^(1/2)) or x = -(((4*229^(1/2)+60)^(1/2))/(2^(1/2)))

x in { ((4*229^(1/2)+60)^(1/2))/(2^(1/2)), -(((4*229^(1/2)+60)^(1/2))/(2^(1/2))) }

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