Question

rezolvati in R ecuatia : 2^2x+1 - 5×2^x + 2 = 0

Answer 1

2^2x·2-5·2^x+2=0
notam 2^x=t
2t²-5t+2=0
Δ=25-16=9
t1=(5-3)/4=2/4=1/2
t2=(5+3)/4=8/4=2
daca t1=1/2=2⁻¹
2^x=2⁻¹
x=-1
daca t2=2
2^x=2
x=1
x∈{-1,1}