Question

$\frac{1}{2} lg(x+9)+lg\sqrt{2x-1} =1$

Answer 1

Объяснение:

$\frac{1}{2} lg(x + 9) + lg \sqrt{2x - 1} = 1 \\ x + 9 > 0 \\ x > - 9 \\ 2x - 1 > 0 \\ x > \frac{1}{2} \\ \frac{1}{2} (lg(x + 9) + lg(2x - 1)) = 1 \\ lg(x + 9) (2x - 1) = 2 \\ lg(2 {x}^{2} + 17x - 9) = lg100 \\ 2 {x}^{2} + 17x - 9 = 100 \\ 2 {x}^{2} + 17x - 109 = 0 \\ d = 289 + 872 = 1161 \\ x1 = \frac{ - 17 + 3 \sqrt{129} }{4} ≈4,2 \\ x2 = \frac{ - 17 - 3 \sqrt{129} }{4}$

x2≈-12- не удовлетворяет одз