1) 3x^2 - 7x+4=0 2) y^2 - 10y-24=0 3) 5x^2=9x+2 4) 15y^2-30=22y+7 5) (x+4) ^2=3x+40 6) 12x^2+7x=0

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Тимур Павлов

Математика

31 августа, 06:32

1) 3x^2 - 7x+4=0 2) y^2 - 10y-24=0 3) 5x^2=9x+2 4) 15y^2-30=22y+7 5) (x+4) ^2=3x+40 6) 12x^2+7x=0

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Квикли · Answer 1

1) 3x² - 7x + 4 = 0;

Д = - 7² - 4 * 3 * 4 = 49 - 48 = 1.

x₁ = (7 - √1) / (3 * 2) = (7 - 1) / 6 = 6/6 = 1.

x₂ = (7 + √1) / (3 * 2) = (7 + 1) / 6 = 8/6 = 4/3.

2) y² - 10y - 24 = 0;

y₁ + у₂ = 10;

у₁ * у₂ = - 24;

у₁ = 12, у₂ = - 2;

3) 5x² = 9x + 2;

5 х² - 9 х - 2 = 0;

Д = - 9² + 4 * 5 * 2 = 81 + 40 = 121.

x₁ = (9 - √121) / (5 * 2) = (9 - 11) / 10 = - 2/10 = - 1/5.

x₂ = (9 + √121) / (5 * 2) = (9 + 11) / 10 = 20/10 = 2.

4) 15y² - 30 = 22y + 7;

15 у² - 22 у - 37 = 0;

Д = 484 + 4 * 15 * 37 = 484 + 2220 = 2704.

x₁ = (30 - √2704) / (15 * 2) = (30 - 52) / 30 = - 22/30 = - 11/15.

x₂ = (30 + √2704) / (15 * 2) = (30 + 52) / 30 = - 82/30 = - 41/15.

5) (x + 4) ² = 3x + 40;

х² - 5 х - 24 = 0;

Д = 25 + 4 * 24 = 25 + 96 = 121.

x₁ = (5 - √121) / (1 * 2) = (5 - 11) / 2 = - 6/2 = - 3.

x₂ = (5 + √121) / (1 * 2) = (5 + 11) / 2 = 16/2 = 8.

6) 12x² + 7x = 0;

х * (12 х + 7) = 0;

х = 0 или 12x + 7 = 0;

12x = - 7;

x = - 7/12.