7(x+(1)/(x))-2(x^2+(1)/(x^2))=9

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Solution for 7(x+(1)/(x))-2(x^2+(1)/(x^2))=9 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)

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

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

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

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

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

7*x-2*x^2+7*x^-1-2*x^-2-9 = 0

7*x-2*x^2+7*x^-1-2*x^-2-9 = 0

7*x^1-2*x^2+7*x^-1-2*x^-2-9*x^0 = 0

(7*x^3-2*x^4-9*x^2+7*x^1-2*x^0)/(x^2) = 0 // * x^4

x^2*(7*x^3-2*x^4-9*x^2+7*x^1-2*x^0) = 0

x^2

7*x^3-2*x^4-9*x^2+7*x-2 = 0

{ 1, -1, 2, -2 }

1

x = 1

7*x^3-2*x^4-9*x^2+7*x-2 = 1

1

-1

x = -1

7*x^3-2*x^4-9*x^2+7*x-2 = -27

-1

2

x = 2

7*x^3-2*x^4-9*x^2+7*x-2 = 0

2

x-2

3*x^2-2*x^3-3*x+1

7*x^3-2*x^4-9*x^2+7*x-2

x-2

2*x^4-4*x^3

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

6*x^2-3*x^3

7*x-3*x^2-2

3*x^2-6*x

x-2

2-x

0

3*x^2-2*x^3-3*x+1 = 0

{ 1, -1 }

1

x = 1

3*x^2-2*x^3-3*x+1 = -1

1

-1

x = -1

3*x^2-2*x^3-3*x+1 = 9

-1

{ 1/2, -1/2, -1/2, 1/2 }

1/2

x

1/2

3*x^2-2*x^3-3*x+1 = 0

1/2

x-1/2

2*x-2*x^2-2

3*x^2-2*x^3-3*x+1

x-1/2

2*x^3-x^2

2*x^2-3*x+1

x-2*x^2

1-2*x

2*x-1

0

2*x-2*x^2-2 = 0

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

DELTA = -12

DELTA < 0

x in { 2, 1/2} 

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

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

( x-1/2 )

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

x = 1/2

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 1/2, 2 }

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