Решите уравнение: 1) 3^2 − 18 = 0; 3) x^2 − x − 20 = 0; 5) x^2 + 6x − 2 = 0; 2) 8^2 − 3x...

1) 3x² - 18 = 0

3x² = 18

x² = 6

x₁ = √6 x₂ = - √6

2) 8x² - 3x = 0

x(8x - 3) = 0

x₁ = 0 8x - 3 = 0

8x = 3

x₂ = 0,375

3) x² - x - 20 = 0

По теореме Виета :

x₁ + x₂ = 1 x₁ * x₂ = - 20 , значит :

x₁ = 5 x₂ = - 4

4) 3x² - 2x - 8 = 0

D = (- 2)² - 4 * 3 * (- 8) = 4 + 96 = 100 = 10²

$x_{1}=\frac{2-10}{6}=-1\frac{1}{3}\\\\x_{2}=\frac{2+10}{6}=2$

5) x² + 6x - 2 = 0

D = 6² - 4 * (- 2) = 36 + 8 = 44 = (2√11)²

$x_{1}=\frac{-6-2\sqrt{11} }{2}=-3-\sqrt{11} \\\\x_{2}=\frac{-6+2\sqrt{11} }{2}=\sqrt{11}-3$

6) x² - 4x + 6 = 0

D = (-4)² - 4 * 6 = 16 - 24 = - 8 < 0

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