Question

решите неравенство 10х(х-1)>(х+1)^2-5 подробно

Answer 1

$10x(x-1)>(x+1)^{2} - 5\\10x^{2} - 10x > x^{2} + 2x + 1 - 5\\10x^{2} - 10x > x^{2} + 2x - 4\\10x^{2} - x^{2} - 10x - 2x + 4 > 0\\9x^{2} - 12x + 4 > 0\\(3x-2)^{2} > 0\\f(x) = (3x-2)^{2}\\f(x) = 0\\(3x-2)^{2} = 0\\3x - 2 = 0\\3x = 2\\x = \frac{2}{3}$

x∈(-∞; $\frac{2}{3}$) ∪ ($\frac{2}{3}$; +∞)