Решить квадратное уравнение 6x²+x-1=0 5x27x+2=0 2x²-9x+4= 0 2x² +3x-5=0 -x²+7x-10=0 3x² + 8x-3=0 2x²-5x+3=9 2x²-7x+3=0 5x²-3x-2=0 3x²+2x-5=0

Решим данные квадратные уравнения.

1. 6x² + x - 1 = 0
   • D = 1² - 4 * 6 * (-1) = 1 + 24 = 25
   • x₁ = (-1 + √25) / (2 * 6) = (-1 + 5) / 12 = 4 / 12 = 1 / 3
   • x₂ = (-1 - √25) / (2 * 6) = (-1 - 5) / 12 = -6 / 12 = -1 / 2

   Ответ: x₁ = 1/3, x₂ = -1/2

2. 5x² - 7x + 2 = 0
   • D = (-7)² - 4 * 5 * 2 = 49 - 40 = 9
   • x₁ = (7 + √9) / (2 * 5) = (7 + 3) / 10 = 10 / 10 = 1
   • x₂ = (7 - √9) / (2 * 5) = (7 - 3) / 10 = 4 / 10 = 2 / 5

   Ответ: x₁ = 1, x₂ = 2/5

3. 2x² - 9x + 4 = 0
   • D = (-9)² - 4 * 2 * 4 = 81 - 32 = 49
   • x₁ = (9 + √49) / (2 * 2) = (9 + 7) / 4 = 16 / 4 = 4
   • x₂ = (9 - √49) / (2 * 2) = (9 - 7) / 4 = 2 / 4 = 1 / 2

   Ответ: x₁ = 4, x₂ = 1/2

4. 2x² + 3x - 5 = 0
   • D = 3² - 4 * 2 * (-5) = 9 + 40 = 49
   • x₁ = (-3 + √49) / (2 * 2) = (-3 + 7) / 4 = 4 / 4 = 1
   • x₂ = (-3 - √49) / (2 * 2) = (-3 - 7) / 4 = -10 / 4 = -5 / 2

   Ответ: x₁ = 1, x₂ = -5/2

5. -x² + 7x - 10 = 0
   • D = 7² - 4 * (-1) * (-10) = 49 - 40 = 9
   • x₁ = (-7 + √9) / (2 * (-1)) = (-7 + 3) / (-2) = -4 / (-2) = 2
   • x₂ = (-7 - √9) / (2 * (-1)) = (-7 - 3) / (-2) = -10 / (-2) = 5

   Ответ: x₁ = 2, x₂ = 5

6. 3x² + 8x - 3 = 0
   • D = 8² - 4 * 3 * (-3) = 64 + 36 = 100
   • x₁ = (-8 + √100) / (2 * 3) = (-8 + 10) / 6 = 2 / 6 = 1 / 3
   • x₂ = (-8 - √100) / (2 * 3) = (-8 - 10) / 6 = -18 / 6 = -3

   Ответ: x₁ = 1/3, x₂ = -3

7. 2x² - 5x + 3 = 9
   • 2x² - 5x - 6 = 0
   • D = (-5)² - 4 * 2 * (-6) = 25 + 48 = 73
   • x₁ = (5 + √73) / (2 * 2) = (5 + √73) / 4
   • x₂ = (5 - √73) / (2 * 2) = (5 - √73) / 4

   Ответ: x₁ = (5 + √73) / 4, x₂ = (5 - √73) / 4

8. 2x² - 7x + 3 = 0
   • D = (-7)² - 4 * 2 * 3 = 49 - 24 = 25
   • x₁ = (7 + √25) / (2 * 2) = (7 + 5) / 4 = 12 / 4 = 3
   • x₂ = (7 - √25) / (2 * 2) = (7 - 5) / 4 = 2 / 4 = 1 / 2

   Ответ: x₁ = 3, x₂ = 1/2

9. 5x² - 3x - 2 = 0
   • D = (-3)² - 4 * 5 * (-2) = 9 + 40 = 49
   • x₁ = (3 + √49) / (2 * 5) = (3 + 7) / 10 = 10 / 10 = 1
   • x₂ = (3 - √49) / (2 * 5) = (3 - 7) / 10 = -4 / 10 = -2 / 5

   Ответ: x₁ = 1, x₂ = -2/5

10. 3x² + 2x - 5 = 0
    • D = 2² - 4 * 3 * (-5) = 4 + 60 = 64
    • x₁ = (-2 + √64) / (2 * 3) = (-2 + 8) / 6 = 6 / 6 = 1
    • x₂ = (-2 - √64) / (2 * 3) = (-2 - 8) / 6 = -10 / 6 = -5 / 3

    Ответ: x₁ = 1, x₂ = -5/3