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Математика1 x² + 8 x - 33=0 2 x² + 12 x - 64 = 0 3 x²-11 x +30=0 4 x² + 14 x + 24 = 0 5 x² - x - 20 = 0 6 x²+x-30=0 7 x²- x - 12 = 0 8 x²-7 x + 12 = 0 9 x²- 2,4 x-13 = 0 10 x²- 5,6 x + 6,4 = 0 11 x²+2,5 x +1 = 0 12 x²-4,5 x + 4,5 = 0 13 - x²+2x+8=0 14 - x²+7x-10=0 15 - x² + 7x +8=0 16 - x²-2x+15=0 17 3x²- 5x-2=0 18 4 x²+x-3=0 19 2 x² - 7x+6=0 20 5x²- 8x+3=0 21 10 x²-3x-1=0 22 3x² + 11 x +6=0 23 3 x²+2x-8=0 24 4 x²-17x-15=0 25 x (x + 2) =3 26 x(x+3)=4 27 x(x-5) = - 4 28 x (x-4) = - 3 29 x (2 x + 1) = 3x + 4 30 x (2x-3) = 4x - 3
Ответ:
Задача: Решить данные квадратные уравнения.
Предмет: Математика, Алгебра
Класс: 8-9
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x² + 8x - 33 = 0
D = 8² - 4 * 1 * (-33) = 64 + 132 = 196
x₁ = (-8 + √196) / 2 = (-8 + 14) / 2 = 6 / 2 = 3
x₂ = (-8 - √196) / 2 = (-8 - 14) / 2 = -22 / 2 = -11
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x² + 12x - 64 = 0
D = 12² - 4 * 1 * (-64) = 144 + 256 = 400
x₁ = (-12 + √400) / 2 = (-12 + 20) / 2 = 8 / 2 = 4
x₂ = (-12 - √400) / 2 = (-12 - 20) / 2 = -32 / 2 = -16
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x² - 11x + 30 = 0
D = (-11)² - 4 * 1 * 30 = 121 - 120 = 1
x₁ = (11 + √1) / 2 = (11 + 1) / 2 = 12 / 2 = 6
x₂ = (11 - √1) / 2 = (11 - 1) / 2 = 10 / 2 = 5
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x² + 14x + 24 = 0
D = 14² - 4 * 1 * 24 = 196 - 96 = 100
x₁ = (-14 + √100) / 2 = (-14 + 10) / 2 = -4 / 2 = -2
x₂ = (-14 - √100) / 2 = (-14 - 10) / 2 = -24 / 2 = -12
-
x² - x - 20 = 0
D = (-1)² - 4 * 1 * (-20) = 1 + 80 = 81
x₁ = (1 + √81) / 2 = (1 + 9) / 2 = 10 / 2 = 5
x₂ = (1 - √81) / 2 = (1 - 9) / 2 = -8 / 2 = -4
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x² + x - 30 = 0
D = 1² - 4 * 1 * (-30) = 1 + 120 = 121
x₁ = (-1 + √121) / 2 = (-1 + 11) / 2 = 10 / 2 = 5
x₂ = (-1 - √121) / 2 = (-1 - 11) / 2 = -12 / 2 = -6
-
x² - x - 12 = 0
D = (-1)² - 4 * 1 * (-12) = 1 + 48 = 49
x₁ = (1 + √49) / 2 = (1 + 7) / 2 = 8 / 2 = 4
x₂ = (1 - √49) / 2 = (1 - 7) / 2 = -6 / 2 = -3
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x² - 7x + 12 = 0
D = (-7)² - 4 * 1 * 12 = 49 - 48 = 1
x₁ = (7 + √1) / 2 = (7 + 1) / 2 = 8 / 2 = 4
x₂ = (7 - √1) / 2 = (7 - 1) / 2 = 6 / 2 = 3
-
x² - 2.4x - 13 = 0
D = (-2.4)² - 4 * 1 * (-13) = 5.76 + 52 = 57.76
x₁ = (2.4 + √57.76) / 2 = (2.4 + 7.6) / 2 = 10 / 2 = 5
x₂ = (2.4 - √57.76) / 2 = (2.4 - 7.6) / 2 = -5.2 / 2 = -2.6
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x² - 5.6x + 6.4 = 0
D = (-5.6)² - 4 * 1 * 6.4 = 31.36 - 25.6 = 5.76
x₁ = (5.6 + √5.76) / 2 = (5.6 + 2.4) / 2 = 8 / 2 = 4
x₂ = (5.6 - √5.76) / 2 = (5.6 - 2.4) / 2 = 3.2 / 2 = 1.6
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x² + 2.5x + 1 = 0
D = (2.5)² - 4 * 1 * 1 = 6.25 - 4 = 2.25
x₁ = (-2.5 + √2.25) / 2 = (-2.5 + 1.5) / 2 = -1 / 2 = -0.5
x₂ = (-2.5 - √2.25) / 2 = (-2.5 - 1.5) / 2 = -4 / 2 = -2
-
x² - 4.5x + 4.5 = 0
D = (-4.5)² - 4 * 1 * 4.5 = 20.25 - 18 = 2.25
x₁ = (4.5 + √2.25) / 2 = (4.5 + 1.5) / 2 = 6 / 2 = 3
x₂ = (4.5 - √2.25) / 2 = (4.5 - 1.5) / 2 = 3 / 2 = 1.5
-
-x² + 2x + 8 = 0
x² - 2x - 8 = 0
D = (-2)² - 4 * 1 * (-8) = 4 + 32 = 36
x₁ = (2 + √36) / 2 = (2 + 6) / 2 = 8 / 2 = 4
x₂ = (2 - √36) / 2 = (2 - 6) / 2 = -4 / 2 = -2
-
-x² + 7x - 10 = 0
x² - 7x + 10 = 0
D = (-7)² - 4 * 1 * 10 = 49 - 40 = 9
x₁ = (7 + √9) / 2 = (7 + 3) / 2 = 10 / 2 = 5
x₂ = (7 - √9) / 2 = (7 - 3) / 2 = 4 / 2 = 2
-
-x² + 7x + 8 = 0
x² - 7x - 8 = 0
D = (-7)² - 4 * 1 * (-8) = 49 + 32 = 81
x₁ = (7 + √81) / 2 = (7 + 9) / 2 = 16 / 2 = 8
x₂ = (7 - √81) / 2 = (7 - 9) / 2 = -2 / 2 = -1
-
-x² - 2x + 15 = 0
x² + 2x - 15 = 0
D = 2² - 4 * 1 * (-15) = 4 + 60 = 64
x₁ = (-2 + √64) / 2 = (-2 + 8) / 2 = 6 / 2 = 3
x₂ = (-2 - √64) / 2 = (-2 - 8) / 2 = -10 / 2 = -5
-
3x² - 5x - 2 = 0
D = (-5)² - 4 * 3 * (-2) = 25 + 24 = 49
x₁ = (5 + √49) / (2 * 3) = (5 + 7) / 6 = 12 / 6 = 2
x₂ = (5 - √49) / (2 * 3) = (5 - 7) / 6 = -2 / 6 = -1/3
-
4x² + x - 3 = 0
D = 1² - 4 * 4 * (-3) = 1 + 48 = 49
x₁ = (-1 + √49) / (2 * 4) = (-1 + 7) / 8 = 6 / 8 = 3/4
x₂ = (-1 - √49) / (2 * 4) = (-1 - 7) / 8 = -8 / 8 = -1
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2x² - 7x + 6 = 0
D = (-7)² - 4 * 2 * 6 = 49 - 48 = 1
x₁ = (7 + √1) / (2 * 2) = (7 + 1) / 4 = 8 / 4 = 2
x₂ = (7 - √1) / (2 * 2) = (7 - 1) / 4 = 6 / 4 = 3/2
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5x² - 8x + 3 = 0
D = (-8)² - 4 * 5 * 3 = 64 - 60 = 4
x₁ = (8 + √4) / (2 * 5) = (8 + 2) / 10 = 10 / 10 = 1
x₂ = (8 - √4) / (2 * 5) = (8 - 2) / 10 = 6 / 10 = 3/5
-
10x² - 3x - 1 = 0
D = (-3)² - 4 * 10 * (-1) = 9 + 40 = 49
x₁ = (3 + √49) / (2 * 10) = (3 + 7) / 20 = 10 / 20 = 1/2
x₂ = (3 - √49) / (2 * 10) = (3 - 7) / 20 = -4 / 20 = -1/5
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3x² + 11x + 6 = 0
D = 11² - 4 * 3 * 6 = 121 - 72 = 49
x₁ = (-11 + √49) / (2 * 3) = (-11 + 7) / 6 = -4 / 6 = -2/3
x₂ = (-11 - √49) / (2 * 3) = (-11 - 7) / 6 = -18 / 6 = -3
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3x² + 2x - 8 = 0
D = 2² - 4 * 3 * (-8) = 4 + 96 = 100
x₁ = (-2 + √100) / (2 * 3) = (-2 + 10) / 6 = 8 / 6 = 4/3
x₂ = (-2 - √100) / (2 * 3) = (-2 - 10) / 6 = -12 / 6 = -2
-
4x² - 17x - 15 = 0
D = (-17)² - 4 * 4 * (-15) = 289 + 240 = 529
x₁ = (17 + √529) / (2 * 4) = (17 + 23) / 8 = 40 / 8 = 5
x₂ = (17 - √529) / (2 * 4) = (17 - 23) / 8 = -6 / 8 = -3/4
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x(x + 2) = 3
x² + 2x - 3 = 0
D = 2² - 4 * 1 * (-3) = 4 + 12 = 16
x₁ = (-2 + √16) / 2 = (-2 + 4) / 2 = 2 / 2 = 1
x₂ = (-2 - √16) / 2 = (-2 - 4) / 2 = -6 / 2 = -3
-
x(x + 3) = 4
x² + 3x - 4 = 0
D = 3² - 4 * 1 * (-4) = 9 + 16 = 25
x₁ = (-3 + √25) / 2 = (-3 + 5) / 2 = 2 / 2 = 1
x₂ = (-3 - √25) / 2 = (-3 - 5) / 2 = -8 / 2 = -4
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x(x - 5) = -4
x² - 5x + 4 = 0
D = (-5)² - 4 * 1 * 4 = 25 - 16 = 9
x₁ = (5 + √9) / 2 = (5 + 3) / 2 = 8 / 2 = 4
x₂ = (5 - √9) / 2 = (5 - 3) / 2 = 2 / 2 = 1
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x(x - 4) = -3
x² - 4x + 3 = 0
D = (-4)² - 4 * 1 * 3 = 16 - 12 = 4
x₁ = (4 + √4) / 2 = (4 + 2) / 2 = 6 / 2 = 3
x₂ = (4 - √4) / 2 = (4 - 2) / 2 = 2 / 2 = 1
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x(2x + 1) = 3x + 4
2x² + x - 3x - 4 = 0
2x² - 2x - 4 = 0
x² - x - 2 = 0
D = (-1)² - 4 * 1 * (-2) = 1 + 8 = 9
x₁ = (1 + √9) / 2 = (1 + 3) / 2 = 4 / 2 = 2
x₂ = (1 - √9) / 2 = (1 - 3) / 2 = -2 / 2 = -1
-
x(2x - 3) = 4x - 3
2x² - 3x - 4x + 3 = 0
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: Выше приведены решения всех уравнений.
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