(8p-8/p-8)(p-8/p-1)

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Solution for (8p-8/p-8)(p-8/p-1) equation: 


D( p )

p = 0

p = 0

p = 0

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

(8*p-(8/p)-8)*(p-(8/p)-1) = 0

(8*p-8*p^-1-8)*(p-8*p^-1-1) = 0

8*p-8*p^-1-8 = 0

8*(p-p^-1-1) = 0

1*p^1-1*p^-1-1*p^0 = 0

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

p^1*(1*p^2-1*p^1-1*p^0) = 0

p^1

p^2-p-1 = 0

p^2-p-1 = 0

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

DELTA = 5

DELTA > 0

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

p = (5^(1/2)+1)/2 or p = (1-5^(1/2))/2

p in { (1-5^(1/2))/2, (5^(1/2)+1)/2} 

8*(p-((1-5^(1/2))/2))*(p-((5^(1/2)+1)/2)) = 0

p-8*p^-1-1 = 0

1*p^1-8*p^-1-1*p^0 = 0

(1*p^2-1*p^1-8*p^0)/(p^1) = 0 // * p^2

p^1*(1*p^2-1*p^1-8*p^0) = 0

p^1

p^2-p-8 = 0

p^2-p-8 = 0

DELTA = (-1)^2-(-8*1*4)

DELTA = 33

DELTA > 0

p = (33^(1/2)+1)/(1*2) or p = (1-33^(1/2))/(1*2)

p = (33^(1/2)+1)/2 or p = (1-33^(1/2))/2

p in { (1-33^(1/2))/2, (33^(1/2)+1)/2} 

(p-((1-33^(1/2))/2))*(p-((33^(1/2)+1)/2)) = 0

8*(p-((1-5^(1/2))/2))*(p-((5^(1/2)+1)/2))*(p-((1-33^(1/2))/2))*(p-((33^(1/2)+1)/2)) = 0

( p-((1-33^(1/2))/2) )

p-((1-33^(1/2))/2) = 0 // + (1-33^(1/2))/2

p = (1-33^(1/2))/2

( p-((1-5^(1/2))/2) )

p-((1-5^(1/2))/2) = 0 // + (1-5^(1/2))/2

p = (1-5^(1/2))/2

( p-((33^(1/2)+1)/2) )

p-((33^(1/2)+1)/2) = 0 // + (33^(1/2)+1)/2

p = (33^(1/2)+1)/2

( p-((5^(1/2)+1)/2) )

p-((5^(1/2)+1)/2) = 0 // + (5^(1/2)+1)/2

p = (5^(1/2)+1)/2

p in { (1-33^(1/2))/2, (1-5^(1/2))/2, (33^(1/2)+1)/2, (5^(1/2)+1)/2 }

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