Question

Алгебра кто знает надеюсь видно это максимальное фото​

Answer 1

1.

$(x - 5)(x + 1)(3x - 6) = 0 \\ x - 5 = 0 \\ x1 = 5 \\ \\ x + 1 = 0 \\ x2 = - 1 \\ \\ 3x - 6 = 0 \\ x3 = 2$

ответ; -1; 2; 5.

2.

$x( {x}^{2} - 4) = 0 \\ \\ x1 = 0 \\ \\ {x}^{2} - 4 = 0 \\ x2 = 2 \\ x3 = - 2$

ответ: -2; 0; 2.

3.

$( {x}^{2} + 49)(x + 3) = 0 \\ \\ {x}^{2} + 49 = 0$

нет корней

$x + 3 = 0 \\ x = - 3$

4.

$(2x - 4)( {x}^{3} - 1) = 0 \\ \\ 2x - 4 = 0 \\ x1 = 2 \\ \\ {x}^{3} - 1 = 0 \\ x2 = 1$

ответ: 1; 2.

5.

$( {x}^{2} + 1)( {x}^{2} - 25) = 0 \\ \\ {x}^{2} + 1 = 0$

нет корней

${x}^{2} - 25 = 0 \\ x1 = 5 \\ x2 = - 5$

ответ: 5; -5.

6.

$2 {x}^{4} - {x}^{3} = 0 \\ {x}^{3}(2x - 1) = 0 \\ \\ {x}^{3} = 0 \\ x1 = 0 \\ \\ 2x - 1 = 0 \\ x2 = \frac{1}{2}$

ответ: 0; 1/2.

7.

$6 {x}^{4} - 3 {x}^{3} + 12 {x}^{2} - 6x = 0 \\ x(6 {x}^{3} - 3 {x}^{2} + 12x - 6) = 0 \\ x(3 {x}^{2} (2x - 1) + 6(2x - 1) )= 0 \\ x(2x - 1)(3 {x}^{2} + 6) = 0 \\ \\ x1 = 0 \\ \\ 2x - 1 = 0 \\ x = \frac{1}{2} \\ \\ 3 {x}^{2} + 6 = 0$

нет корней

ответ: 0; 1/2.

8.

${x}^{3} - 7x + 6 = 0 \\ {x}^{3} - x -6 x + 6 = 0 \\ x( {x}^{2} - 1) - 6(x + 1) = 0 \\ x(x - 1)(x + 1) - 6(x + 1) = 0 \\ (x + 1)(x(x - 1) - 6) = 0 \\ (x + 1)( {x}^{2} - x - 6) = 0 \\ \\ x + 1 = 0 \\ x1 = - 1 \\ \\ {x}^{2} - x - 6 = 0 \\ d = 1 + 24 = 25 \\ x1 = \frac{1 + 5}{2} = 3 \\ x2 = - 2$

ответ: -2; -1; 3.

9.

${x}^{4} + 2 {x}^{3} + 5 {x}^{2} + 4x - 12 = 0 \\ {x}^{4} - {x}^{3} + 3 {x}^{3} - 3 {x}^{2} + 8 {x}^{2} - 8x + 12x - 12 = 0 \\ {x}^{3} (x - 1) + 3 {x}^{2} (x - 1) + 8x(x - 1) + 12(x - 1) = 0 \\ (x - 1)( {x}^{3} + 3 {x}^{2} + 8x + 12) = 0 \\ (x - 1)( {x}^{3} + 2 {x}^{2} + {x}^{2} + 2x + 6x + 12) = 0 \\ (x - 1)( {x}^{2} (x + 2) + x(x + 2) + 6(x + 2)) = 0 \\ (x - 1)(x + 2)( {x}^{2} + x + 6) = 0 \\ \\ x - 1 = 0 \\ x1 = 1 \\ \\ x + 2 = 0 \\ x2 = - 2 \\ \\ {x}^{2} + x + 6 = 0$

нет корней

ответ: -2; 1.