Реши примеры: 1) \( 1^2 - 400 \) 2) \( D = b^2 - 4ac \) 3) \( x_1 = \frac{-b - \sqrt{D}}{2a} \) 4) \( x_2 = \frac{-b + \sqrt{D}}{2a} \) Реши уравнения: 1) \( 5x^2 + 9x + 4 = 0 \) 2) \( y^2 - 12y + 32 = 0 \) 3) \( x^2 - 26x + 25 = 0 \) 4) \( 3p^2 - 10p + 3 = 0 \) 5) \( x^2 + 2x - 80 = 0 \)

Решение:

Примеры:

1) \( 1^2 - 400 = 1 - 400 = -399 \)

2) \( D = b^2 - 4ac \)

3) \( x_1 = \frac{-b - \sqrt{D}}{2a} \)

4) \( x_2 = \frac{-b + \sqrt{D}}{2a} \)

Уравнения:

1) \( 5x^2 + 9x + 4 = 0 \)

• \( a=5, b=9, c=4 \)
• \( D = 9^2 - 4 · 5 · 4 = 81 - 80 = 1 \)
• \( x_1 = \frac{-9 - \sqrt{1}}{2 · 5} = \frac{-9 - 1}{10} = \frac{-10}{10} = -1 \)
• \( x_2 = \frac{-9 + \sqrt{1}}{2 · 5} = \frac{-9 + 1}{10} = \frac{-8}{10} = -0.8 \)

2) \( y^2 - 12y + 32 = 0 \)

• \( a=1, b=-12, c=32 \)
• \( D = (-12)^2 - 4 · 1 · 32 = 144 - 128 = 16 \)
• \( y_1 = \frac{12 - \sqrt{16}}{2} = \frac{12 - 4}{2} = \frac{8}{2} = 4 \)
• \( y_2 = \frac{12 + \sqrt{16}}{2} = \frac{12 + 4}{2} = \frac{16}{2} = 8 \)

3) \( x^2 - 26x + 25 = 0 \)

• \( a=1, b=-26, c=25 \)
• \( D = (-26)^2 - 4 · 1 · 25 = 676 - 100 = 576 \)
• \( x_1 = \frac{26 - \sqrt{576}}{2} = \frac{26 - 24}{2} = \frac{2}{2} = 1 \)
• \( x_2 = \frac{26 + \sqrt{576}}{2} = \frac{26 + 24}{2} = \frac{50}{2} = 25 \)

4) \( 3p^2 - 10p + 3 = 0 \)

• \( a=3, b=-10, c=3 \)
• \( D = (-10)^2 - 4 · 3 · 3 = 100 - 36 = 64 \)
• \( p_1 = \frac{10 - \sqrt{64}}{2 · 3} = \frac{10 - 8}{6} = \frac{2}{6} = \frac{1}{3} \)
• \( p_2 = \frac{10 + \sqrt{64}}{2 · 3} = \frac{10 + 8}{6} = \frac{18}{6} = 3 \)

5) \( x^2 + 2x - 80 = 0 \)

• \( a=1, b=2, c=-80 \)
• \( D = 2^2 - 4 · 1 · (-80) = 4 + 320 = 324 \)
• \( x_1 = \frac{-2 - \sqrt{324}}{2} = \frac{-2 - 18}{2} = \frac{-20}{2} = -10 \)
• \( x_2 = \frac{-2 + \sqrt{324}}{2} = \frac{-2 + 18}{2} = \frac{16}{2} = 8 \)

Ответ: 1) \( -399 \)

Ответ: 2) \( D = b^2 - 4ac \)

Ответ: 3) \( x_1 = \frac{-b - \sqrt{D}}{2a} \)

Ответ: 4) \( x_2 = \frac{-b + \sqrt{D}}{2a} \)

Ответ: 1) \( x_1 = -1, x_2 = -0.8 \)

Ответ: 2) \( y_1 = 4, y_2 = 8 \)

Ответ: 3) \( x_1 = 1, x_2 = 25 \)

Ответ: 4) \( p_1 = \frac{1}{3}, p_2 = 3 \)

Ответ: 5) \( x_1 = -10, x_2 = 8 \)