Question

РЕШИТЕ СРОЧНО ДАЮ 20 БАЛЛОВ
Розв'язати рiвняння

1) 5x² - 10 = 0;

2) x²+ 4x = 0;

3) 3х² + 7x + 2 = 0;

4) x² - 8x + 16 = 0;

5) x²+ x + 3 = 0;

6) 3х²-x-5=0.

Answer 1

1)

$5 {x}^{2} - 10 = 0 \\ \\ 5( {x}^{2} - 2) = 0 \\ \\ {x}^{2} - 2 = 0 \\ \\ {x}^{2} = 2 \\ \\ x = \sqrt{2 } \\ x = - \sqrt{2}$

2)

${x}^{2} + 4x = 0 \\ \\ x(x + 4) = 0 \\ \\ x = 0 \\ \\ x + 4 = 0 \\ x = - 4$

3)

$3 {x}^{2} + 7x + 2 = 0 \\ \\ d = 49 - 24 = 25 \\ \\ x1 = \frac{ - 7 + 5}{6} = - \frac{1}{3} \\ \\ x2 = \frac{ - 7 - 5}{6} = - 2$

4)

${x}^{2} - 8x + 16 = 0 \\ \\ {(x - 4)}^{2} = 0 \\ \\ x - 4 = 0 \\ \\ x = 4$

5)

${x}^{2} + x + 3 = 0 \\ \\ d = 1 - 12 = - 11$

корней нет

6)

$3 {x}^{2} - x - 5 = 0 \\ \\ d = 1 + 60 = 61 \\ \\ x1 = \frac{1 - \sqrt{61} }{6} \\ \\ x2 = \frac{1 + \sqrt{61} }{6}$