Question

Rezolvati : lgx+ 1 pe lgx = 2 10 PUNCTEEE

Answer 1

DVA:x>0 si x ≠1
lg^2x+1=2lgx⇔lg^2x-2lgx+1=0⇔(lgx-1)^2=0⇔lgx-1=0⇔lgx=1⇔x=10

Answer 2

incepe cu DVA: x>0=>x∈(0;∞)
lgx +1/lgx =2
inmultim  ecuatia cu lgx si obtinem (lgx)² + 1 =2lgx
Notam: lgx=y
y²+1=2y
y²-2y+1=0
Utilizam relatiile lui Viete
$\left \{ {{y_{1} } + y_{1}=2 \atop {y_ {1} } * y_{1} =1$
de aici reiese ca y1,2=1
Revenim la notatie: lgx=1=>lgx=lg10=>x=10
x=10∈DVA
S={10}