| a) (x + 5)² + 11 = 10(x + 10) |
| x² + 10x + 25 + 11 = 10x + 100 |
| x² + 36 = 100 |
| x² = 64 |
| x1,2 = ±√64 = ±8 |
| x1 = 8 und x2 = -8 |
| |
| b) (3 - 3x)(8x + 8) = 12x² + 20 |
| 24x + 24 - 24x² - 24x = 12x² + 20 |
| - 24x² + 24 = 12x² + 20 |
| 4 = 36x² |
| x² = 9 |
| x1 = 3 und x2 = -3 |
| |
| c) (x + 3)² + (x - 3)² = 90 |
| x² + 6x + 9 + x² - 6x + 9 = 90 |
| 2x² + 18 = 90 |
| 2x² = 72 |
| x² = 36 |
| x1 = 6 und x2 = -6 |
| |
| d) (x + 4)(x - 4) - 8x = (2x - 2)² - 47 |
| x² - 4x + 4x - 16 - 8x = 4x² - 8x + 4 - 47 |
| x² - 8x - 16 = 4x² - 8x - 43 |
| x² - 16 = 4x² - 43 |
| 27 = 3x² |
| x² = 9 |
| x1 = 3 und x2 = -3 |
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