Question

Решите уравнение 2^2x-5*2^x+4=0
СРОЧНО!!

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.