Решите уравнение: 1) 7x² – 21 = 0; 2) 5x²+ 9x = 0; 3) x² + x – 42 = 0; 4) 3x² – 28x + 9 = 0; 5) 2x² – 8x + 11 = 0; 6) 16x² – 8x + 1 = 0.

1) 7x² – 21 = 0

• 7x² = 21
• x² = 3
• x = ±√3

2) 5x² + 9x = 0

• x(5x + 9) = 0
• x = 0 или 5x + 9 = 0
• x = 0 или x = -9/5 = -1.8

3) x² + x – 42 = 0

• По теореме Виета: x₁ + x₂ = -1, x₁ * x₂ = -42
• Подбираем корни: x₁ = -7, x₂ = 6

4) 3x² – 28x + 9 = 0

• D = (-28)² – 4 * 3 * 9 = 784 – 108 = 676
• x₁ = (28 + √676) / (2 * 3) = (28 + 26) / 6 = 54 / 6 = 9
• x₂ = (28 - √676) / (2 * 3) = (28 - 26) / 6 = 2 / 6 = 1/3

5) 2x² – 8x + 11 = 0

• D = (-8)² – 4 * 2 * 11 = 64 – 88 = -24
• D < 0, корней нет

6) 16x² – 8x + 1 = 0

• (4x – 1)² = 0
• 4x – 1 = 0
• x = 1/4 = 0.25

Ответ:

1) x = ±√3

2) x = 0, x = -1.8

3) x = -7, x = 6

4) x = 9, x = 1/3

5) корней нет

6) x = 0.25