| a) x²/4 + 3/2 x + 2 = 0 |
| HN: 4 = 2 * 2 |
| x² + 6x + 8 = 0 |
| x1,2 = -6/2 ± √((6/2)² - 8) = -3 ± √(1) = -3 ± 1 |
| x1 = -2 |
| x2 = -4 |
| L = {-2;-4} |
| |
| b) 1/10 x² = 5 + x/2 |
| HN: 10 = 2 * 5 |
| x² = 50 + 5x |
| x² - 5x - 50 = 0 |
| x1,2 = 5/2 ± √((-5/2)² + 50) = 5/2 ± √(25/4 + 50) |
| = 5/2 ± √(225/4) |
| = 5/2 ± 15/2 |
| x1 = 10 |
| x2 = -5 |
| L = {10;-5} |
| |
| c) x²/9 - 1/2 = x/3 + 3/2 |
| HN: 18 = 2 * 9 |
| 2x² - 9 = 6x + 27 |
| 2x² - 6x - 36 = 0 |
| x1,2 = (6 ± √((-6)² - 4 * 2 * (-36))) / 4 = (6 ± √(36 + 288)) / 4 |
| = (6 ± √(324)) / 4 = (6 ± 18) / 4 |
| x1 = (6 + 18) / 4 = 6 |
| x2 = (6 - 18) / 4 = -3 |
| L = {6;-3} |
| |
| d) 1/2 x² + (9x + 9)/4 = 0 |
| HN: 4 = 2 * 2 |
| 2x² + 9x + 9 = 0 |
| x1,2 = (-9 ± √(9² - 4 * 2 * 9)) / 4 = (-9 ± √(81 - 72)) / 4 |
| = (-9 ± √(9)) / 4 = (-9 ± 3) / 4 |
| x1 = (-9 + 3) / 4 = -6/4 = -3/2 |
| x2 = (-9 - 3) / 4 = -12/4 = -3 |
| L = {-1,5;-3} |
| |
| e) (x² + 4)/6 + 4/3 x = x/2 |
| HN: 6 = 2 * 3 |
| x² + 4 + 8x = 3x |
| x² + 5x + 4 = 0 |
| x1,2 = -5/2 ± √((5/2)² - 4) = -5/2 ± √(9/4) = -5/2 ± 3/2 |
| x1 = -1 |
| x2 = -4 |
| L = {-1;-4} |
| |
| f) (x² - 6)/6 + 1/3 x = 1/2 x |
| HN: 6 = 2 * 3 |
| x² - 6 + 2x = 3x |
| x² - x - 6 = 0 |
| x1,2 = 1/2 ± √((1/2)² + 6) = 1/2 ± √(25/4) = 1/2 ± 5/2 |
| x1 = 3 |
| x2 = -2 |
| L = {3;-2} |
|
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