Question

Помогите пожалуйста решить 10 уравнений!! 35 баллов

Answer 1

1)

$8 {a}^{2} - 14a + 5 = 0 \\ D = {( - 14)}^{2} - 4 \times 8 \times 5 = 196 - 160 = 36 \\ \sqrt{D} = \sqrt{36} = 6 \\ x1 = \frac{14 + 6}{2 \times 8} = \frac{20}{16} = 1.25 \\ x2 = \frac{14 - 6}{2 \times 8} = \frac{8}{16} = 0.5$

Ответ: 1,25; 0,5

2)

$4 {x}^{2} - 2x + 3 = 0 \\ D = {( - 2)}^{2} - 4 \times 4 \times 3 = 4 - 48 = - 44$

Ответ: нет корней

3)

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

Ответ: 0; -2

4)

$7 {x}^{2} - 28 = 0 \\ 7( {x}^{2} - 4) = 0 \\ {x}^{2} - 4 = 0 \\ {x}^{2} = 4 \\ x = \sqrt{4} \: \: \: \: \: \: \: \: \: x = - \sqrt{4} \\ x = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 2$

Ответ: 2; -2

5)

$3 {x}^{2} - 5x + 2 = 0 \\ D = {( - 5)}^{2} - 4 \times 3 \times 2 = 25 - 24 = 1 \\ \sqrt{D} = \sqrt{1} = 1 \\ x1 = \frac{5 + 1}{2 \times 3} = \frac{6}{6} = 1 \\ x2 = \frac{5 - 1}{ 2 \times 3} = \frac{4}{6} = \frac{2}{3}$

Ответ: 1; 2/3

6)

$6 {x}^{2} - 12 = 0 \\ 6 {x}^{2} = 12 \\ {x}^{2} = \frac{12}{6} \\ {x}^{2} = 2 \\ x = \sqrt{2} \\ x = - \sqrt{2}$

Ответ: √2, -√2

7)

$3 {a}^{2} + 5a + 2 = 0 \\ D = {5}^{2} - 4 \times 3 \times 2 = 25 - 24 = 1 \\ \sqrt{D} = \sqrt{1} = 1 \\ x1 = \frac{ - 5 + 1}{2 \times 3} = \frac{ - 4}{6} = - \frac{2}{3} \\ x2 = \frac{ - 5 - 1}{2 \times 3} = \frac{ - 6}{6} = - 1$

Ответ: -2/3; -1

8)

$3 {x}^{2} - 24x + 45 = 0 \: \: \: | \: \div 3 \\ {x}^{2} - 8x + 15 = 0 \\ D = {( - 8)}^{2} - 4 \times 1 \times 15 = 64 - 60 = 4 \\ \sqrt{D} = \sqrt{4} = 2 \\ x1 = \frac{ 8 + 2}{2 \times 1} = \frac{10}{2} = 5 \\ x2 = \frac{8 - 2}{2 \times 1} = \frac{6}{2} = 3$

Ответ: 5; 3

9)

$4x + 4 {x}^{2} + 1 = 0 \\ 4 {x}^{2} + 4x + 1 = 0 \\ D = {4}^{2} - 4 \times 4 \times 1 = 16 - 16 = 0 \\ x = \frac{ - 4}{2 \times 4} = \frac{ - 4}{8} = - 0.5$

10)

$3 {x}^{2} + 7x - 6 = 0 \\ D = {7}^{2} - 4 \times 3 \times ( - 6) = 49 + 72 = 121 \\ \sqrt{D} = \sqrt{121} = 11 \\ x1 = \frac{ - 7 + 11}{2 \times 3} = \frac{4}{6} = \frac{2}{3} \\ x2 = \frac{ - 7 - 11}{2 \times 3} = \frac{ - 18}{6} = - 3$

Ответ: 2/3; -3