3 equations that should have some relationships; 3 equations of this thread so far.

In[14]:= soln = Solve[y == Sqrt[(n*y - x^2)/x], x]
soln //. {n -> 85, y -> 16.85229955} // N
Out[14]= {{x -> 1/2 (-y^2 - Sqrt[4 n y + y^4])}, {x ->
1/2 (-y^2 + Sqrt[4 n y + y^4])}}
Out[15]= {{x -> -288.957}, {x -> 4.95729}}

Sqrt[(85*(85/x) – x^2)/ x] = x

Abs(tan(85 / (2*Pi))) * x + x = 85/(2*Pi) tan in radians of course.

((85^4/x + 2*(85^2 * x^2) + x^5) / 85^3 ) * x – 85 = 0

These 3 equations each approximate x and y when 85 = x * y.

In my program I tested each value from 1 to 85 to see which numbers worked for x.

There is some error, but it x should approximately equal 5.

N = p *q or N = x * y.

I cannot solve the polynomial to find x from only knowing N. But when you test y proves the equation works.

The trouble is it is not so much different from factoring. No speed increase. But it is a legitimate equation. I am researching new ways to solve polynomials.

Any more questions just ask or see my site: www.constructorscorner.net

There is a link on the Homepage ?