Question

Решите квадратное уравнение без дискриминанта!!!
(6 - 2x)^2 = 3x - 9

Answer 1

Ответ:

3; 3,75

Объяснение:

$(6 - 2x) {}^{2} = 3x - 9 \\ 36 - 24x + 4x {}^{2} = 3x - 9 \\ 36 - 24x + 4x {}^{2} - 3x + 9 = 0 \\ 45 - 27x + 4x {}^{2} = 0 \\ 4x {}^{2} - 27x + 45 = 0 \\ 4x {}^{2} \underbrace{ - 12x - 15x} _{ - 27x} + 45 = 0 \\ 4x(x - 3) - 15(x - 3) = 0 \\ (x - 3)(4x - 15) = 0 \\ 1) \: x - 3 = 0 \to \: x = 3 \\ 2) \: 4x - 15 = 0 \to \: 4x = 15 \to \: x = \frac{15}{4}$