Question

Решить уравнение, используя теорему Виета
а) х²+5х-14=0
б) х²-7х+12=0
в) х²-8х-9=0
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Answer 1

решение смотри на фотографии

Answer 2

$x {}^{2} + 5x - 14 = 0 \\ d = 5 {}^{2} + 4 \times 1 \times 14 = \sqrt{81} = 9 \\ x1 = \frac{ - 5 + 9}{2} = \frac{4}{2} = 2 \\ x2 = \frac{ - 5 - 9}{2} = \frac{ - 14}{2} = - 7 \\ x1 + x2 = 2 + ( - 7) = - 5 \\ x1 \times x2 = 2 \times ( - 7) = 14$

Объяснение:

$x {}^{2} - 7x + 12 = 0 \\ d = 7 {}^{2} - 4 \times 1 \times 12 = 49 - 48 = 1 \\ x1 = \frac{7 + 1}{2} = \frac{8}{2} = 4 \\ x2 = \frac{7 - 1}{2} = \frac{6}{2} = 3 \\ x1 + x2 = 4 + 3 = 7 \\ x1 \times x2 = 4 \times 3 = 12$

$x {}^{2} - 8x - 9 = 0 \\ d = 8 {}^{2} + 4 \times 1 \times 9 = 64 + 36 = \sqrt{100} = 10 \\ x1 = \frac{8 + 10}{2} = \frac{18}{2} = 9 \\ x2 = \frac{8 - 10}{2} = \frac{ - 2}{2} = - 1 \\ x1 + x2 = 9 + ( - 1) = 8 \\ x1 \times x2 = 9 \times ( - 1) = - 9$