x^2+81/x^2=18

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Solution for x^2+81/x^2=18 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+81/(x^2) = 18 // - 18

x^2+81/(x^2)-18 = 0

x^2+81*x^-2-18 = 0

t_1 = x^2

1*t_1^1+81*t_1^-1-18 = 0

1*t_1^1+81*t_1^-1-18*t_1^0 = 0

(1*t_1^2-18*t_1^1+81*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-18*t_1^1+81*t_1^0) = 0

t_1^1

t_1^2-18*t_1+81 = 0

t_1^2-18*t_1+81 = 0

DELTA = (-18)^2-(1*4*81)

DELTA = 0

t_1 = 18/(1*2)

t_1 = 9 or t_1 = 9

t_1 in { 9, 9} 

t_1 = 9

x^2-9 = 0

1*x^2 = 9 // : 1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

t_1 = 9

x^2-9 = 0

1*x^2 = 9 // : 1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

x in { 3, -3, 3, -3 }

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