Question

Розв'яжіть рівняння (2х-1)^4 - 26(2x - 1)^2 + 25 = 0​

Answer 1

Ответ:

${(2x - 1)}^{4} - 26 {(2x - 1)}^{2} + 25 = 0 \\ \\ {(2x - 1)}^{2} = t \\ \\ t {}^{2} - 26 t + 25 = 0 \\ d = 676 - 100 = 576 \\ t1 = \frac{26 + 24}{2} = 25 \\ t2 = 1 \\ \\ {(2x - 1)}^{2} = 25 \\ 4 {x}^{2} - 4x + 1 = 25 \\ 4 {x}^{2} - 4x - 24 = 0 \\ {x}^{2} - x - 6 = 0 \\ D= 1 + 24 = 25 \\ x_1 = \frac{1 + 5}{2} = 3 \\ x_2 = - 2 \\ \\ {(2x - 1)}^{2} = 1 \\ 4 {x}^{2} - 4x + 1 = 1 \\ 4 {x}^{2} - 4x = 0 \\ 4x(x - 1) = 0 \\ x3 = 0 \\ x4 = 1$

Ответ: -2; 0; 1; 3.

Answer 2

Ответ:

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