x2-4/x=17

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Solution for x2-4/x=17 equation: 


D( x )

x = 0

x = 0

x = 0

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

x^2-(4/x) = 17 // - 17

x^2-(4/x)-17 = 0

x^2-4*x^-1-17 = 0

1*x^2-4*x^-1-17*x^0 = 0

(1*x^3-17*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^3-17*x^1-4*x^0) = 0

x^1

x^3-17*x-4 = 0

{ 1, -1, 2, -2, 4, -4 }

1

x = 1

x^3-17*x-4 = -20

1

-1

x = -1

x^3-17*x-4 = 12

-1

2

x = 2

x^3-17*x-4 = -30

2

-2

x = -2

x^3-17*x-4 = 22

-2

4

x = 4

x^3-17*x-4 = -8

4

-4

x = -4

x^3-17*x-4 = 0

-4

x+4

x^2-4*x-1

x^3-17*x-4

x+4

-x^3-4*x^2

-4*x^2-17*x-4

4*x^2+16*x

-x-4

x+4

0

x^2-4*x-1 = 0

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

DELTA = 20

DELTA > 0

x = (20^(1/2)+4)/(1*2) or x = (4-20^(1/2))/(1*2)

x = (2*5^(1/2)+4)/2 or x = (4-2*5^(1/2))/2

x in { (4-2*5^(1/2))/2, (2*5^(1/2)+4)/2, -4} 

x in { (4-2*5^(1/2))/2, (2*5^(1/2)+4)/2, -4 }

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