Question

lg la patrat din x +4lgx +3=0

Answer 1

lg²x+4lg x+3=0
Punem conditia de existenta a logaritmului: x>0.
Notam lg x=t si ecuatia devine:
t²+4t+3=0
Observam ca ecuatia poate fi scrisa astfel:
(t+1)(t+3)=0
t1=-1
t2=-3
Daca nu iti dai seama de descompunere, calculezi Δ.
Δ=4²-4*3=16-12=4
t1=-4+2/2=-2/2=-1
t2=-4-2/2=-6/2=-3

Cazul 1: Daca t=-1, atunci lg x=-1. Deci x=10^-1=1/10.
Cazul 2: Daca t=-3, atunci lg x=-3. Deci x=10^-3=1/10^3=1/1000.