x^2+1/x^2=66

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Solution for x^2+1/x^2=66 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) = 66 // - 66

x^2+1/(x^2)-66 = 0

x^2+x^-2-66 = 0

t_1 = x^2

1*t_1^1+1*t_1^-1-66 = 0

1*t_1^1+1*t_1^-1-66*t_1^0 = 0

(1*t_1^2-66*t_1^1+1*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-66*t_1^1+1*t_1^0) = 0

t_1^1

t_1^2-66*t_1+1 = 0

t_1^2-66*t_1+1 = 0

DELTA = (-66)^2-(1*1*4)

DELTA = 4352

DELTA > 0

t_1 = (4352^(1/2)+66)/(1*2) or t_1 = (66-4352^(1/2))/(1*2)

t_1 = (16*17^(1/2)+66)/2 or t_1 = (66-16*17^(1/2))/2

t_1 in { (66-16*17^(1/2))/2, (16*17^(1/2)+66)/2} 

t_1 = (66-16*17^(1/2))/2

x^2-((66-16*17^(1/2))/2) = 0

1*x^2 = (66-16*17^(1/2))/2 // : 1

x^2 = (66-16*17^(1/2))/2

x^2 = (66-16*17^(1/2))/2 // ^ 1/2

abs(x) = ((66-16*17^(1/2))^(1/2))/(2^(1/2))

x = ((66-16*17^(1/2))^(1/2))/(2^(1/2)) or x = -(((66-16*17^(1/2))^(1/2))/(2^(1/2)))

t_1 = (16*17^(1/2)+66)/2

x^2-((16*17^(1/2)+66)/2) = 0

1*x^2 = (16*17^(1/2)+66)/2 // : 1

x^2 = (16*17^(1/2)+66)/2

x^2 = (16*17^(1/2)+66)/2 // ^ 1/2

abs(x) = ((16*17^(1/2)+66)^(1/2))/(2^(1/2))

x = ((16*17^(1/2)+66)^(1/2))/(2^(1/2)) or x = -(((16*17^(1/2)+66)^(1/2))/(2^(1/2)))

x in { ((66-16*17^(1/2))^(1/2))/(2^(1/2)), -(((66-16*17^(1/2))^(1/2))/(2^(1/2))), ((16*17^(1/2)+66)^(1/2))/(2^(1/2)), -(((16*17^(1/2)+66)^(1/2))/(2^(1/2))) }

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