Решите уравнения: 1) 2x^2 - 3x + 5 =0 2) x^2 + 8x + 16 =0 3) 3x^2 - 2x - 5 =0 4) x^2 - 2x - 4 =0 5) x^2 -√3x - 1 =0

1) 2x² - 3x + 5 = 0
D = b² - 4ac = 9 - 4 × 2 × 5 = 9 - 40 = - 31 - корней нет.

2) x² + 8x + 16 = 0
D = b² - 4ac = 64 - 4 × 16 = 64 - 64 = 0 - имеет один корень
x = - b/2a
x = - 8/2 = - 4

3) 3x² - 2x - 5 = 0
D = b² - 4ac = 4 - 4 × 3 × (-5) = 4 + 60 = 64 = 8²
x1 = ( 2 + 8) / 6 = 10/6 = 5/3 = 1 2/3
x2 = ( 2 - 8) / 6 = - 1

4) x² - 2x - 4 = 0
D = b² - 4ac = 4 - 4 × (-4) = 4 + 16 = 20
x1 = ( 2 + 2√5) / 2 = 2( 1 + √5) / 2 = 1 + √5
x2 = ( 2 - 2√5) / 2 = 2( 1 - √5) / 2 = 1 - √5

5) x² - √3x - 1 = 0
- √3x - 1 = - x²
√3x - 1 = x²
3x - 1 = (x²)²
3x - 1 = x⁴
- x⁴ + 3x - 1 = 0
x⁴ - 3x + 1 = 0