Question

Задание 1.

Решите уравнения:

x^2 − 9x + 20 = 0
21x^2 − 2x − 3 = 0
(3x + 1)(9x^2 − 3x + 1) − (9x^2 + 2)(3x − 2) = 16x^2 + 1

Answer 1

${x}^{2} - 9x + 20 = 0 \\ x(1) = 5 \\ x(2) = 4$

$21 {x}^{2} - 2x - 3 = 0 \\ {x}^{2} - 2x - (3 \times 21) = 0 \\ {x}^{2} - 2x - 63 = 0 \\ 21x(1) = 9 \\ 21x(2) = - 7 \\ x(1) = \frac{9}{21} = \frac{3}{7} \\ x(2) = \frac{ - 7}{21} = \frac{ - 1}{3}$

$(3x + 1)(9 {x}^{2} - 3x + 1) - (9 {x}^{2} + 2)(3x - 2) = 16 {x}^{2} + 1 \\ 27 {x}^{3} + 1 - 27 {x}^{3} + 18 {x}^{2} - 6x + 4 - 16 {x}^{2} - 1 = 0 \\ 2 {x}^{2} - 6x + 4 = 0 \\ {x}^{2} - 3x + 2 = 0 \\ d = 9 - 8 = 1 \\ x(1) = 2 \\ x(2) = 1$

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