Question

1) 5x^2-11x+1=0
2) 5x^2-7x+3=0
3) 81y^2+18y-1=0
4) 4x^2+x-33=0
СРОЧНО

Answer 1

Ответ:

1

$5 {x}^{2} - 11x + 1 = 0 \\ D= {11}^{2} - 4 \times 5 = 121 - 20 = 101 \\ x_1 = \frac{11 + \sqrt{101} }{5 \times 2} = \frac{11 + \sqrt{101} }{10} \\ x_2 = \frac{11 - \sqrt{101} }{10}$

2

$5 {x}^{2} - 7x + 3 = 0 \\ D= {7}^{2} - 4 \times 3 \times 5 = 49 - 60 = - 11 \\ D < 0$

корней нет

3

$81 {y}^{2} + 18y - 1 = 0 \\ D= {18}^{2} + 4 \times 81 = 324 + 324 = \\ = 2 \times 324 \\ y_1 = \frac{ - 18 + \sqrt{2 \times 324} }{2 \times 81} = \frac{ - 18 + 18 \sqrt{2} }{162} \\ y_2 = \frac{ - 18 - 18 \sqrt{2} }{162}$

4

$4 {x}^{2} + x - 33 = 0 \\ D = 1 + 4 \times 4 \times 33 = 1 + 528 = 529 \\ x_1 = \frac{ - 1 + \sqrt{529} }{4 \times 2} = \frac{ - 1 + 23}{8} = \frac{22}{8} = \frac{11}{4} \\ x_2 = - \frac{24}{8} = - 3$