Question

Решите уравнение
15х²=8х-1
​

Answer 1

$15x {}^{2} = 8x - 1 \\ 15x {}^{2} - 8x + 1 = 0 \\ 15x {}^{2} - 3x - 5x + 1 = 0 \\ 3x(5x - 1) - (5 x - 1) = 0 \\ (3x - 1)(5x - 1) = 0$

1)

$3x - 1 = 0 \\ 3x = 1 \\ x = \frac{1}{3}$

2)

$5x - 1 = 0 \\ 5x = 1 \\ x = 0.2$

ответ:

$x1 =0.2 \\ x2 = \frac{1}{3}$

Answer 2

15х² = 8х - 1

15х² - 8х + 1 = 0

D = b² - 4ac = (-8)² - 4 · 15 · 1 = 64 - 60 = 4

√D = √4 = 2

х₁ = (8-2)/(2·15) = 6/30 = 1/5

х₂ = (8+2)/(2·15) = 10/30 = 1/3

Ответ: (1/5; 1/3).