Question

Rezolvati in multimea numerelor reale ecuatia lg^2 x^2 + 3lg 1/x =1

Answer 1

conditia de existenta a logaritmilor x>0
(lgx²)²+3lgx⁻¹=1
(2lgx)²-3lgx=1
4lg²x-3lgx-1=0
notam lgx=t
4t²-3t-1=0
Δ=9-4x4x(-1)=25, Δ=5
t1=(3+5)/2=8/2=4, lgx=4, x=10⁴
t2=(3-5)/2=-1, lgx=-1, x=10⁻¹=1/10