x+1/x=51/5

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Solution for x+1/x=51/5 equation: 


D( x )

x = 0

x = 0

x = 0

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

x+1/x = 51/5 // - 51/5

x+1/x-(51/5) = 0

x+1/x-51/5 = 0

1*x^1+1*x^-1-51/5*x^0 = 0

(1*x^2-51/5*x^1+1*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-51/5*x^1+1*x^0) = 0

x^1

x^2+(-51/5)*x+1 = 0

x^2+(-51/5)*x+1 = 0

DELTA = (-51/5)^2-(1*1*4)

DELTA = 2501/25

DELTA > 0

x = ((2501/25)^(1/2)-(-51/5))/(1*2) or x = (-(-51/5)-(2501/25)^(1/2))/(1*2)

x = ((2501/25)^(1/2)+51/5)/2 or x = (51/5-(2501/25)^(1/2))/2

x in { (51/5-(2501/25)^(1/2))/2, ((2501/25)^(1/2)+51/5)/2} 

x in { (51/5-(2501/25)^(1/2))/2, ((2501/25)^(1/2)+51/5)/2 }

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