Find the equilibria of the Ostwald ripening model we have been discussing, 
i.e. find the roots of the equation 

              μ x3 + c* exp( γ/x ) = c1 ,   where  c1 := c0 + μ (x*)3. 

Parameter values: μ=1.e-3, c*=7.52e-7, γ=4.e-3, c0= 1.05 c*.

For a specified x* (see below),  your code should solve the equation for x 
(by calling your Newton solver), and print it out. 
[ Do NOT confuse the initial value x* with initial guess(es) for Newton Method ! ]

Find the roots x1 and x2 (at full double precision: 15 decimals)

1: when x* = 0.05 ;    verify that x1 < x2 < x* ;
2: when x* = 0.0975 ;  verify that x1 < x* < x2;
3: when x* = 0.08 and μ=1.e-5 ; verify that x* < x1 < x2.

Discuss the physical meaning of these results for the Ostwald Ripening model 
and what theory predicts for each case.

Submit ONLY the following: 

roots and discussion
==========================================================
your main program (that calls your Newton solver)
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your FCN subprogram

NOTE: 
 The parameters pertain only to the function, so should be entered in the FCN subprogram.
 You cannot use " * " in variable names in a code!
     Could use "xstar", "cstar", or some other reasonable names...