Question

după acest model trebuie sa rezolv : 2lgx pe
lg(5x-4)=1 Vă rog ​

Answer 1

Răspuns:

$\frac{2lgx}{lg(5x-4)}$ = 1

C.E: 5x - 4  > 0 => 5x > -4 => x > $\frac{-4}{5}$ => x ∈ (  $\frac{-4}{5}$ , + ∝ )

2lgx = lg ( 5x - 4 )

lg x² = lg ( 5x - 4 )

5x - 4 = x²

x² - 5x + 4 = 0

Δ = b² - 4ac = 25 - 16 = 9

x₁ = ( -b + √Δ ) / 2a = ( 5 + 3 ) / 2 = 8 / 2 = 4

x₂ = ( -b - √Δ ) / 2a = ( 5 - 3 ) / 2 = 2 / 2 = 1

S = { 1, 4 } ∈ (  $\frac{-4}{5}$ , + ∝ )