Question

2^x+2^-x=5/2 cat face chestia asta

Answer 1

2^x +2^(-x)=5/2



notam 2^x=t ⇒2^(-x)= 1/2^x=1/t
atunci avem ecuatia
t+1/t=5/2
aducem la acvelasi numitor si amplificam cu  t>0

t²+1=5t/2

2t²-5t+2=0
 Δ=25-16=9

t1,2 =( 5+/-3)/4

t1=2
t2=-1/2

2^x=2⇒ x=1
2^x =1/2 ⇒ x=-1
S={-1;1}