Вариант 6: x²=7x+18 7x² + 9x + 2 = 0 x²-5x+6=0.

Вариант 6

1. \( x^2 = 7x + 18 \)
2. \( x^2 - 7x - 18 = 0 \)
3. \( D = (-7)^2 - 4 \cdot 1 \cdot (-18) = 49 + 72 = 121 \)
4. \( x_1 = \frac{7 + \sqrt{121}}{2} = \frac{7 + 11}{2} = 9 \)
5. \( x_2 = \frac{7 - \sqrt{121}}{2} = \frac{7 - 11}{2} = -2 \)
6. \( 7x^2 + 9x + 2 = 0 \)
7. \( D = 9^2 - 4 \cdot 7 \cdot 2 = 81 - 56 = 25 \)
8. \( x_1 = \frac{-9 + \sqrt{25}}{2 \cdot 7} = \frac{-9 + 5}{14} = -\frac{4}{14} = -\frac{2}{7} \)
9. \( x_2 = \frac{-9 - \sqrt{25}}{2 \cdot 7} = \frac{-9 - 5}{14} = -\frac{14}{14} = -1 \)
10. \( x^2 - 5x + 6 = 0 \)
11. \( D = (-5)^2 - 4 \cdot 1 \cdot 6 = 25 - 24 = 1 \)
12. \( x_1 = \frac{5 + \sqrt{1}}{2} = \frac{5 + 1}{2} = 3 \)
13. \( x_2 = \frac{5 - \sqrt{1}}{2} = \frac{5 - 1}{2} = 2 \)

Ответ: Вариант 6: x₁ = 9, x₂ = -2; x₁ = -2/7, x₂ = -1; x₁ = 3, x₂ = 2.