1) 10 х² - 3 х - 0,4=02) 7 х² - 6 х-1=03) 1+8 х - 9 х²4) х² + 12=7 х

Question

Арсений Федоров

Математика

29 января, 21:29

1) 10 х² - 3 х - 0,4=02) 7 х² - 6 х-1=03) 1+8 х - 9 х²4) х² + 12=7 х

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Мирон Пономарев · Answer 1

1)

10x² - 3x - 0,4 = 0;

x² - 3/10 x - 4/100 = 0;

D = (-3/10) ² - 4 * (-4/100) = 9/100 + 16/100 = 25/100;

x₁ = ( - (-3/10) + √ (25/100)) / 2 = (3/10 + 5/10) / 2 = 4/10 = 0,4;

x₂ = ( - (-3/10) - √ (25/100)) / 2 = (3/10 - 5/10) / 2 = - 1/10 = - 0,1;

x₁ = 0,4;

x₂ = - 0,1.

2)

7x² - 6x - 1 = 0;

D = (-6) ² - 4 * 7 * (-1) = 36 + 28 = 64;

x₁ = ( - (-6) + √64) / (2 * 7) = (6 + 8) / 14 = 14 / 14 = 1;

x₂ = ( - (-6) - √64) / (2 * 7) = (6 - 8) / 14 = - 2 / 14 = - 1/7;

x₁ = 1;

x₂ = - 1/7.

3)

1 + 8x - 9x² = 0;

9x² - 8x - 1 = 0;

D = (-8) ² - 4 * 9 * (-1) = 64 + 36 = 100;

x₁ = ( - (-8) + √100) / (2 * 9) = (8 + 10) / 18 = 18 / 18 = 1;

x₂ = ( - (-8) - √100) / (2 * 9) = (8 - 10) / 18 = - 2 / 18 = - 1/9;

x₁ = 1;

x₂ = - 1/9;

1 + 8x - 9x² = - (9x² - 8x - 1) = - (x - 1) (x + 1/9) = (1 - x) (x + 1/9).

4)

x² + 12 = 7x;

x² - 7x + 12 = 0;

D = (-7) ² - 4 * 12 = 49 - 48 = 1;

x₁ = ( - (-7) + √1) / 2 = (7 + 1) / 2 = 8 / 2 = 4;

x₂ = ( - (-7) - √1) / 2 = (7 - 1) / 2 = 6 / 2 = 3;

x₁ = 4;

x₂ = 3.