(1/x^2)+x^2=62

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Solution for (1/x^2)+x^2=62 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) = 62 // - 62

x^2+1/(x^2)-62 = 0

x^2+x^-2-62 = 0

t_1 = x^2

1*t_1^1+1*t_1^-1-62 = 0

1*t_1^1+1*t_1^-1-62*t_1^0 = 0

(1*t_1^2-62*t_1^1+1*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-62*t_1^1+1*t_1^0) = 0

t_1^1

t_1^2-62*t_1+1 = 0

t_1^2-62*t_1+1 = 0

DELTA = (-62)^2-(1*1*4)

DELTA = 3840

DELTA > 0

t_1 = (3840^(1/2)+62)/(1*2) or t_1 = (62-3840^(1/2))/(1*2)

t_1 = (16*15^(1/2)+62)/2 or t_1 = (62-16*15^(1/2))/2

t_1 in { (62-16*15^(1/2))/2, (16*15^(1/2)+62)/2} 

t_1 = (62-16*15^(1/2))/2

x^2-((62-16*15^(1/2))/2) = 0

1*x^2 = (62-16*15^(1/2))/2 // : 1

x^2 = (62-16*15^(1/2))/2

x^2 = (62-16*15^(1/2))/2 // ^ 1/2

abs(x) = ((62-16*15^(1/2))^(1/2))/(2^(1/2))

x = ((62-16*15^(1/2))^(1/2))/(2^(1/2)) or x = -(((62-16*15^(1/2))^(1/2))/(2^(1/2)))

t_1 = (16*15^(1/2)+62)/2

x^2-((16*15^(1/2)+62)/2) = 0

1*x^2 = (16*15^(1/2)+62)/2 // : 1

x^2 = (16*15^(1/2)+62)/2

x^2 = (16*15^(1/2)+62)/2 // ^ 1/2

abs(x) = ((16*15^(1/2)+62)^(1/2))/(2^(1/2))

x = ((16*15^(1/2)+62)^(1/2))/(2^(1/2)) or x = -(((16*15^(1/2)+62)^(1/2))/(2^(1/2)))

x in { ((62-16*15^(1/2))^(1/2))/(2^(1/2)), -(((62-16*15^(1/2))^(1/2))/(2^(1/2))), ((16*15^(1/2)+62)^(1/2))/(2^(1/2)), -(((16*15^(1/2)+62)^(1/2))/(2^(1/2))) }

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