System of two polynomial equations

Question

I am stuck at solving these equations and any help would be appreciated. I don't really care about how the solution would look like as I will be using a program to solve it:

$x_1= (1-2x_1-3x_2)^{6.6}$

$x_2= (1-2x_1-3x_2)^{6.2}$

Edit: I tried dividing the two equations, but couldn't make it work. Also I could try having the first equation in root of $6.6$ on both sides. Then I can easily find $x_2$ , however when I plug it in the second equation it just gets uglier and uglier.

Answer 1

Let $1-2x_1-3x_2=t^5$. Then the two equations become

$$x_1=t^{33}, x_2=t^{32}.$$

This reduces your task to solving the polynomial equation $$t^5=1-2t^{33}-3t^{32}$$ i.e. $$2t^{33}+3t^{32}+t^5-1=0.$$