2(x^2+1/x^2)-9(x+1/x)+14=0

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Solution for 2(x^2+1/x^2)-9(x+1/x)+14=0 equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

2*(x^2+1/(x^2))-(9*(x+1/x))+14 = 0

2*(x^2+1/(x^2))-9*(x+1/x)+14 = 0

2*(x^2+x^-2)-9*(x+x^-1)+14 = 0

2*(x^2+x^-2)-9*(x+x^-1)+14 = 0

2*x^2-9*x-9*x^-1+2*x^-2+14 = 0

2*x^2-9*x-9*x^-1+2*x^-2+14 = 0

2*x^2-9*x^1-9*x^-1+2*x^-2+14*x^0 = 0

(2*x^4-9*x^3+14*x^2-9*x^1+2*x^0)/(x^2) = 0 // * x^4

x^2*(2*x^4-9*x^3+14*x^2-9*x^1+2*x^0) = 0

x^2

2*x^4-9*x^3+14*x^2-9*x+2 = 0

{ 1, -1, 2, -2 }

1

x = 1

2*x^4-9*x^3+14*x^2-9*x+2 = 0

1

x-1

2*x^3-7*x^2+7*x-2

2*x^4-9*x^3+14*x^2-9*x+2

x-1

2*x^3-2*x^4

14*x^2-7*x^3-9*x+2

7*x^3-7*x^2

7*x^2-9*x+2

7*x-7*x^2

2-2*x

2*x-2

0

2*x^3-7*x^2+7*x-2 = 0

{ 1, -1, 2, -2 }

1

x = 1

2*x^3-7*x^2+7*x-2 = 0

1

x-1

2*x^2-5*x+2

2*x^3-7*x^2+7*x-2

x-1

2*x^2-2*x^3

7*x-5*x^2-2

5*x^2-5*x

2*x-2

2-2*x

0

2*x^2-5*x+2 = 0

DELTA = (-5)^2-(2*2*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)+5)/(2*2) or x = (5-9^(1/2))/(2*2)

x = 2 or x = 1/2

x in { 1/2, 2, 1, 1} 

(x-1/2)*(x-2)*(x-1)^2 = 0

(x-1/2)*(x-2)*(x-1)^2 = 0

( x-1/2 )

x-1/2 = 0 // + 1/2

x = 1/2

( x-1 )

x-1 = 0 // + 1

x = 1

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 1/2, 1, 1, 2 }

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