Question

Найти: x?

(t-x)/5a - 6b = 2k-1

Решить уравнение:

(2x - 3)^2 = 8x^2

Answer 1

$\frac{t-x}{5a - 6b} = 2k-1 \\ t-x =(2k-1)(5a - 6b) \\ x = t - (2k-1)(5a - 6b)$

$(2x - 3)^2 = 8x^2 \\ 4 {x}^{2} - 12x + 9 - 8 {x}^{2} = 0 \\ - 4 {x}^{2} - 12x + 9 = 0 \\ 4 {x}^{2} + 12x - 9 = 0 \\ \\ D= {b}^{2} - 4ac \\ \\ D= {12}^{2} - 4 \times 4 \times ( - 9) = \\ = 144 + 144 = 288 \\ \\ x_{1} = \frac{ - b - \sqrt{D} }{2a} \\ x_{2} = \frac{ - b + \sqrt{D} }{2a} \\ \\ x_{1} = \frac{ - 12 - 12 \sqrt{2} }{2 \times 4} = \frac{ - 3 - 3 \sqrt{2} }{2} \\ x_{2} = \frac{ - 12 + 12 \sqrt{2} }{2 \times 4} = \frac{ - 3 + 3 \sqrt{2} }{2}$

Ответ:

$x_{1} = \frac{ - 3 - 3 \sqrt{2} }{2} \\ x_{2} = \frac{ - 3 + 3 \sqrt{2} }{2}$