Question

Determinati xy daca 2lg(x-12/y)=lg x-lg y , unde x>12/y>0

Answer 1

Răspuns:

xy = 9  ; xy = 16

Explicație pas cu pas:

2lg(x-12/y)=lg x-lg y , unde x>12/y>0

lg(x-12/y)² = lg(x/y) =>

(x-12/y)² = x/y

(xy-12)²/y² = x/y <=>

(xy-12)²/y = x

(xy-12)² = xy

x²y²-24xy+144 = xy <=>

x²y²-25xy+144 = 0

xy = t =>

t²-25t+144 = 0 =>

t₁,₂ = (25±√(625-576)/2

t₁,₂ = (25±7)/2 => t₁ = 9 ; t₂ = 16

xy = 9  ; xy = 16