Question

Para \sf \dpi{90} 1 \neq x \in \mathbb{R}^{*}_{+}, qual é a solução de \sf \dpi{90} x^{\frac{x+3}{3x+2}}=\sqrt{x} ?

S = {1}

S = {2}

S = {3}

S = {4}

S = {5}

Answer 1

x^[(x + 3)/(3x + 2)] = √x

x^[(x + 3)/(3x + 2)] = x^(1/2)

logx x^[(x + 3)/(3x + 2)] = logx x^(1/2)

CONDIÇÃO: 0 < x ≠ 1

(x + 3)/(3x + 2) · logx x = 1/2 · logx x

(x + 3)/(3x + 2) · 1 = 1/2 · 1

(x + 3)/(3x + 2) = 1/2

CONDIÇÃO: x ≠ – 2/3

(3x + 2) · 1 = (x + 3) · 2

3x + 2 = 2x + 6

3x – 2x = 6 – 2

x = 4

Resp: S = {4}

Tuum sincere,

MathSapiens.