Вариант 5: x²=-x+20 5x² - 3x - 2 = 0. x²+7x+6=0

Вариант 5

1. \( x^2 = -x + 20 \)
2. \( x^2 + x - 20 = 0 \)
3. \( D = 1^2 - 4 \cdot 1 \cdot (-20) = 1 + 80 = 81 \)
4. \( x_1 = \frac{-1 + \sqrt{81}}{2} = \frac{-1 + 9}{2} = 4 \)
5. \( x_2 = \frac{-1 - \sqrt{81}}{2} = \frac{-1 - 9}{2} = -5 \)
6. \( 5x^2 - 3x - 2 = 0 \)
7. \( D = (-3)^2 - 4 \cdot 5 \cdot (-2) = 9 + 40 = 49 \)
8. \( x_1 = \frac{3 + \sqrt{49}}{2 \cdot 5} = \frac{3 + 7}{10} = 1 \)
9. \( x_2 = \frac{3 - \sqrt{49}}{2 \cdot 5} = \frac{3 - 7}{10} = -0.4 \)
10. \( x^2 + 7x + 6 = 0 \)
11. \( D = 7^2 - 4 \cdot 1 \cdot 6 = 49 - 24 = 25 \)
12. \( x_1 = \frac{-7 + \sqrt{25}}{2} = \frac{-7 + 5}{2} = -1 \)
13. \( x_2 = \frac{-7 - \sqrt{25}}{2} = \frac{-7 - 5}{2} = -6 \)

Ответ: Вариант 5: x₁ = 4, x₂ = -5; x₁ = 1, x₂ = -0.4; x₁ = -1, x₂ = -6.