Question

Am nevoie de ajutor urgent lg2 x–6 lg x +5= 0 va rog dau coronita ​

Answer 1

Răspuns:

lg 2x - 6 lg x + 5 = 0

2 lg x - 3 lg x² + 5 = 0

Notam lg x cu t, astfel:

-3t² + 2t + 5 = 0

Δ = b² - 4ac = 4 + 60 = 64

x₁ = ( -b + √Δ ) / 2a =  ( -2 + 8 ) / -6 = 6 / -6 = -1

x₂ = ( -b - √Δ ) / 2a =  ( -2 - 8 ) / -6 = -10 / -6 = 10 / 6 = 5 / 3

t = lgx =>

1. lg x = -1 => x = 10⁻¹ = $\frac{1}{10}$

2. lg x = 5 / 3 => x = $10^{5/3}$ = ∛10⁵

=> S = { $\frac{1}{10}$ , ∛10⁵ }

EDIT: lg²x - 6 lgx + 5 = 0

C.E: x > 0, x ≠ 1 => x ∈ ( 0, +∝ ) / { 1 }

Notam lgx cu t, astfel:

t² - 6t + 5 = 0

Δ = b² - 4ac = 36 - 20 = 16

x₁ = ( -b + √Δ ) / 2a = ( 6 + 4 ) / 2 = 10 / 2 = 5

x₂ = ( -b - √Δ ) / 2a = ( 6 - 4 ) / 2 = 2 / 2 = 1

1. lgx = 5 => x = 10⁵

2. lgx = 1 => x = 10

=> S = { 10, 10⁵ } ∈ ( 0, +∝ ) / { 1 }