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i need help with this equation c^2-81/c^2 12c 27


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\ c^2-81/c^2 12c 27

Nov 24th, 2017

I'm assuming the equation you want is:

c^2 -81/c^2 +12c =27

Subtract 27 from both sides.

c^2 -81/c^2 +12c-27=0
Multiply everything by c^2.
c^4 -81+12c^3-27c^2=0
You will now have to do the rational roots test. It will take a while to explain, which unfortunately there is not enough time to do so here. Check: http://www.purplemath.com/modules/solvpoly.htm For an explanation on how to do the rational root test.
Lets rewrite it in a more easy way to work with:
c^4+12c^3-27c^2-81=0
The factors of 81 are 3^4
so lets try c=3 and c=-3 as roots
c=3 works as a root! when we plug it in we get 324-324=0
c=-3  45-243-81=NOT 0
So c=3 is a root.
Lets simplify...
Use long division to factor the original polynomial with (c-3).
Using graphical methods you can find a root exists at c=15.
Taken together we see:

(c-3)(c+15)(c^2+18 +(-216c +729)/(c-3)(c+15)))

Given this, I probably mistook the problem you meant. Post the correct problem and I can solve it.
Jul 31st, 2014

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