Question

ПОМОГИТЕ ПОЖАЛУЙСТА!!!умоляю!!!

Answer 1

$\sqrt{2x - 4} - \sqrt{x + 5} = 1 \\ 2x - 4 + x + 5 - 2 \sqrt{(2x - 4)(x + 5)} = 1 \\ 3x = 2 \sqrt{2 {x}^{2} + 6x - 20 } \\ 9 {x}^{2} = 4(2 {x}^{2} + 6x - 20) \\ 9 {x}^{2} - 8 {x}^{2} - 24x + 80 = 0 \\ {x}^{2} - 24x + 80 = 0 \\ x1 + x2 = 24 \\ x1 \times x2 = 80 \\ x1 = 20 \\ x2 = 4$

Проверим корни

$x = 20 \\ \sqrt{2x - 4} - \sqrt{x + 5} = \sqrt{40 - 4} - \sqrt{20 + 5} = 6 - 5 = 1 \: true \\ x = 4 \\ \sqrt{2 \times 4 - 4} - \sqrt{4 + 5} = 2 - 1 = - 1 false$

Ответ х=20