Question

lg(x+1)-lg(x -1)^2=1

Answer 1

C.E
x>-1
x≠1
deci x∈(-1;∞)\{1}

rezolvare
10^1=(x+1)/(x-1)²

10(x²-2x+1)=x+1
10x²-20x+10=x+1

10x²-21x+9=0

Δ=441-360=81
√Δ=9
x1,2=(21+/-9)/20
x1=30/20=3/2∈Dom.de definitie
x2=12/20=3/5∈Dom de def
S={3/5;3/2}

verificare
 pt x=3/5
 lg(8/5)-lg(4/25)=lg((6/5):(4/25))=lg(8/5*25/4)=lg10=1 corect

pt 3/2
 lg(5/2)-lg(1/4) =lg((5/2)*4))=lg10=1 corect
adevarate ambele, bine rezolvat