Question

2^2x-5*2^x+4=0
пусть t=2x ,
тогда t^2-5t+4=0

Answer 1

2^2x-5*2^x+4=0;
(2^x)^2 - 5* 2^x + 4 = 0
пусть t=2^x ,
тогда t^2-5t+4=0;
D = 25 - 16 = 9= 3^2;
t1 = (5+3) / 2 = 4;
 t2 = (5 - 3)/ 2 = 1;

t = 4; ⇒2^x = 4;
 2^x = 2^2 ;
 x = 2

t = 1 ; ⇒ 2^x = 1;
 2^x = 2^0;
 x = 0.

Ответ х = 0  или х = 2