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Question: Finding root for a complicated term

Question:Finding root for a complicated term

escorpsy 125 Maple
rootof
April 30 2013
1

Hello guys ,

 

i have a complicated function , i found its roots but when i evaluate function by its roots , the result is not zero !!!

 

thank you for your helpWork.mw

> 

f := proc (n) options operator, arrow; -2*n*((-4*n^2+7*n-3)*RootOf((2*n-1)*_Z^2+(6*n-2)*_Z-6*n+6)-11+27*n-16*n^2)/((3-3*n)*((2*n^2-n)*RootOf((2*n-1)*_Z^2+(6*n-2)*_Z-6*n+6)+8*n^2-4*n))+1/3 end proc

proc (n) options operator, arrow; -2*n*((-4*n^2+7*n-3)*RootOf((2*n-1)*_Z^2+(6*n-2)*_Z-6*n+6)-11+27*n-16*n^2)/((3-3*n)*((2*n^2-n)*RootOf((2*n-1)*_Z^2+(6*n-2)*_Z-6*n+6)+8*n^2-4*n))+1/3 end proc

 (1)
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solve({f(n) = 0}, {n})

{n = 1/4+(1/12)*33^(1/2)}, {n = 1/4-(1/12)*33^(1/2)}

 (2)
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f := 2*n/(3-3*n)*(-((-4*n^2+7*n-3)*RootOf((2*n-1)*_Z^2+(6*n-2)*_Z-6*n+6)-11+27*n-16*n^2)/((2*n^2-n)*RootOf((2*n-1)*_Z^2+(6*n-2)*_Z-6*n+6)+8*n^2-4*n))+1/3

-2*n*((-4*n^2+7*n-3)*RootOf((2*n-1)*_Z^2+(6*n-2)*_Z-6*n+6)-11+27*n-16*n^2)/((3-3*n)*((2*n^2-n)*RootOf((2*n-1)*_Z^2+(6*n-2)*_Z-6*n+6)+8*n^2-4*n))+1/3

 (3)
> 

eval(f, [n = 1/4-(1/12)*sqrt(33)])

-2*(1/4-(1/12)*33^(1/2))*((-4*(1/4-(1/12)*33^(1/2))^2-5/4-(7/12)*33^(1/2))*RootOf(-(-3-33^(1/2))*_Z^2-(-3-3*33^(1/2))*_Z-27-3*33^(1/2))-17/4-(9/4)*33^(1/2)-16*(1/4-(1/12)*33^(1/2))^2)/((9/4+(1/4)*33^(1/2))*((2*(1/4-(1/12)*33^(1/2))^2-1/4+(1/12)*33^(1/2))*RootOf(-(-3-33^(1/2))*_Z^2-(-3-3*33^(1/2))*_Z-27-3*33^(1/2))+8*(1/4-(1/12)*33^(1/2))^2-1+(1/3)*33^(1/2)))+1/3

 (4)
> 

s := -(2*(1/4-(1/12)*sqrt(33)))*((-4*(1/4-(1/12)*sqrt(33))^2-5/4-(7/12)*sqrt(33))*RootOf(-(-3-sqrt(33))*_Z^2-(-3-3*sqrt(33))*_Z-27-3*sqrt(33))-17/4-(9/4)*sqrt(33)-16*(1/4-(1/12)*sqrt(33))^2)/((9/4+(1/4)*sqrt(33))*((2*(1/4-(1/12)*sqrt(33))^2-1/4+(1/12)*sqrt(33))*RootOf(-(-3-sqrt(33))*_Z^2-(-3-3*sqrt(33))*_Z-27-3*sqrt(33))+8*(1/4-(1/12)*sqrt(33))^2-1+(1/3)*sqrt(33)))+1/3

-2*(1/4-(1/12)*33^(1/2))*((-4*(1/4-(1/12)*33^(1/2))^2-5/4-(7/12)*33^(1/2))*RootOf(-(-3-33^(1/2))*_Z^2-(-3-3*33^(1/2))*_Z-27-3*33^(1/2))-17/4-(9/4)*33^(1/2)-16*(1/4-(1/12)*33^(1/2))^2)/((9/4+(1/4)*33^(1/2))*((2*(1/4-(1/12)*33^(1/2))^2-1/4+(1/12)*33^(1/2))*RootOf(-(-3-33^(1/2))*_Z^2-(-3-3*33^(1/2))*_Z-27-3*33^(1/2))+8*(1/4-(1/12)*33^(1/2))^2-1+(1/3)*33^(1/2)))+1/3

 (5)
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evalf(s)

-1.372281324

 (6)
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