Question

решить уравнение. ПОМОГИТЕ ПОЖАЛУЙСТА​

Answer 1

Ответ:

1.

${7}^{ - (2 {x}^{2} + x - 0.5) } = {7}^{0.5 - 1} \\ - 2 {x}^{2} - x + 0.5 = - 0.5 \\ - 2 {x}^{2} - x + 1 = 0 \\ 2 {x}^{2} + x - 1 = 0 \\ d = 1 + 8 = 9 \\ x1 = \frac{ - 1 + 3}{4} = 0.5 \\ x2 = - 1$

2.

$3 \times {5}^{x + 3} + 2 \times {5}^{x + 1} = 77 \\ {5}^{x + 1} (3 \times {5}^{2} + 2) = 77 \\ {5}^{x + 1} \times 77 = 77 \\ {5}^{x + 1} = 1 \\ x + 1 = 0 \\ x = - 1$

3.

${49}^{x} - 8 \times {7}^{x} + 7 = 0 \\ {7}^{x} = t \\ {t}^{2} - 8t + 7 = 0 \\ d = 64 - 28 = 36 \\ t1 = \frac{8 + 6}{2} = 7 \\ t2 = 1 \\ \\ {7}^{x} = 7 \\ x1 = 1 \\ \\ {7}^{x} = 1 \\ x2 = 0$

4.

${3}^{2y - x} = \frac{1}{81} \\ {3}^{x - y + 2} = 27 \\ \\ {3}^{2y - x} = {3}^{ - 4} \\ {3}^{x - y + 2} = {3}^{3} \\ \\ 2y - x = - 4 \\ x - y + 2 = 3 \\ \\ x = 2y + 4 \\ x - y = 1 \\ \\ 2y + 4 - y = 1 \\ y = - 3 \\ \\ x = - 6 + 4 = - 2$

Ответ: (-2; -3)