Question

Решить уравнения: 1. 3x2-1=0
2. 2х2-6х=0
3. 8х2=0
4. х2+81=0
5. х2-=0
6. х2=5х
7. х2+х-3=х+6
8. х2=8,1

Answer 1

1.

$3 {x}^{2} - 1 = 0 \\ {x}^{2} = \frac{1}{3} \\ x1 = \sqrt{ \frac{1}{3} } = \frac{ \sqrt{3} }{3} \\ x2 = - \frac{ \sqrt{3} }{3}$

2.

$2 {x}^{2} - 6x = 0 \\ 2x(x - 3) = 0 \\ \\ 2x = 0 \\ x1 = 0 \\ \\ x - 3 = 0 \\ x2 = 3$

3.

$8 {x}^{2} = 0 \\ {x}^{2} = 0 \\ x 1 = x2= 0$

4.

${x}^{2} + 81 = 0 \\ {x}^{2} = - 81$

корней нет, так как - 81 < 0.

5.

${x}^{2} = 0 \\ x = 0$

6.

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

7.

${x}^{2} + x - 3 = x + 6 \\ {x}^{2} + x - 3 - x - 6 = 0 \\ {x}^{2} - 9 = 0 \\ {x}^{2} = 9 \\ \\ x1 = 3 \\ x2 = - 3$

8.

${x}^{2} = 8.1 \\ \\ x1 = \sqrt{8.1} = \sqrt{81 \times 10} = 9 \sqrt{10} \\ x2 = - 9 \sqrt{10}$