Question

rezolvati ecuatia :

lg^2 x^2 + 3lg 1/x = 1

Answer 1

Ecuatia se poate scrie: $(lgx^2)^2+3(lg1-lgx)-1=0,sau,(2lgx)^2-3lgx-1=0,adica$, $4lg^2x-3lgx-1=0,notam,lgx=y,ecuatia,4y^2-3y-1=0,are$, radacinile $y_{1}=1,si, y_{2}=- \frac{1}{4}$, de unde lgx=1 ne da X1=10, iar de la lg=-1/4 rezulta X2=$10^{- \frac{1}{4} }= \frac{1}{ \sqrt[4]{10} } .$