Question

Решите уравнение:
$(x-3)^{3x^{2}-10x+3}=1$

Answer 1

Ответ:

$(x-3)^{3x^{2} - 10x +3} = 1\\\\(x-3)^{3x^{2} - 10x +3} = (x-3)^{0} \\\\3x^{2} - 10x + 3 = 0\\\\D = (-10)^{2} - 4 * 3 * 3 = 100 - 36 = 64\\\\x_{1} = \frac{10 +\sqrt{64} }{6} = \frac{10+8}{6} = \frac{18}{6} = 3\\\\x_{2} = \frac{10 - \sqrt{64} }{2 * 3} = \frac{10 - 8}{6} = \frac{2}{6} = \frac{1}{3}$