Question

Решите уровнение пж
$(x-1)(x-4)x+7=x(x+1) {}^{2}$
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Answer 1

$(x {}^{2} - x) \times (x - 4) + 7 = x \times (x {}^{2} + 2x + 1)$

$x {}^{3} - 4x {}^{2} - x {}^{2} + 4x + 7 = x {}^{3} + 2x {}^{2} + x$

$- 4x {}^{2} - x {}^{2} + 4x + 7 = 2x {}^{2} + x$

$- 5x {}^{2} + 4x + 7 = 2x {}^{2} + 2$

$- 5x {}^{2} + 4x + 7 - 2x {}^{2} - x = 0$

$- 7x {}^{2} + 3x + 7 = 0$

$7x {}^{2} - 3x - 7 = 0 \\ d = ( - 3) {}^{2} - 4 \times 7 \times ( - 7) = 205 \\ x1 = \frac{3 + \sqrt{205} }{14} \\ x2 = \frac{3 - \sqrt{205} }{14}$