x^2+1/x^2=31/9

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Solution for x^2+1/x^2=31/9 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) = 31/9 // - 31/9

x^2+1/(x^2)-(31/9) = 0

x^2+1/(x^2)-31/9 = 0

x^2+x^-2-31/9 = 0

t_1 = x^2

1*t_1^1+1*t_1^-1-31/9 = 0

1*t_1^1+1*t_1^-1-31/9*t_1^0 = 0

(1*t_1^2-31/9*t_1^1+1*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-31/9*t_1^1+1*t_1^0) = 0

t_1^1

t_1^2+(-31/9)*t_1+1 = 0

t_1^2+(-31/9)*t_1+1 = 0

DELTA = (-31/9)^2-(1*1*4)

DELTA = 637/81

DELTA > 0

t_1 = ((637/81)^(1/2)-(-31/9))/(1*2) or t_1 = (-(-31/9)-(637/81)^(1/2))/(1*2)

t_1 = ((637/81)^(1/2)+31/9)/2 or t_1 = (31/9-(637/81)^(1/2))/2

t_1 in { (31/9-(637/81)^(1/2))/2, ((637/81)^(1/2)+31/9)/2} 

t_1 = (31/9-(637/81)^(1/2))/2

x^2-((31/9-(637/81)^(1/2))/2) = 0

1*x^2 = (31/9-(637/81)^(1/2))/2 // : 1

x^2 = (31/9-(637/81)^(1/2))/2

x^2 = (31/9-(637/81)^(1/2))/2 // ^ 1/2

abs(x) = ((31/9-(637/81)^(1/2))^(1/2))/(2^(1/2))

x = ((31/9-(637/81)^(1/2))^(1/2))/(2^(1/2)) or x = -(((31/9-(637/81)^(1/2))^(1/2))/(2^(1/2)))

t_1 = ((637/81)^(1/2)+31/9)/2

x^2-(((637/81)^(1/2)+31/9)/2) = 0

1*x^2 = ((637/81)^(1/2)+31/9)/2 // : 1

x^2 = ((637/81)^(1/2)+31/9)/2

x^2 = ((637/81)^(1/2)+31/9)/2 // ^ 1/2

abs(x) = (((637/81)^(1/2)+31/9)^(1/2))/(2^(1/2))

x = (((637/81)^(1/2)+31/9)^(1/2))/(2^(1/2)) or x = -((((637/81)^(1/2)+31/9)^(1/2))/(2^(1/2)))

x in { ((31/9-(637/81)^(1/2))^(1/2))/(2^(1/2)), -(((31/9-(637/81)^(1/2))^(1/2))/(2^(1/2))), (((637/81)^(1/2)+31/9)^(1/2))/(2^(1/2)), -((((637/81)^(1/2)+31/9)^(1/2))/(2^(1/2))) }

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