Roots of a polynomial

Question

The number of integer x such that x^2x-3(2^x+2)+2⁵ =0

 

Please help with this roots question

Answer 1

I am guessing that the equation is supposed to be: 

 

2^2x - 3(2^x+2) + 2⁵ = 0

 

(2^x)² - 3(2^x)(2²) + 2⁵ = 0

 

(2^x)² - 12(2^x) + 32 = 0

 

Let u = 2^x.  Then, we have u² - 12u + 32 = 0

 

                                     (u - 8)(u - 4) = 0

 

                                         u = 8 or  u = 4

 

2^x = 8 or 2^x = 4    So, x = 3 or x = 2.