Question

Сколько целочисленных решений имеет неравенство 15-x^2+10x> 0?

Answer 1

$15-x^2+10x\ \textgreater \ 0\\\\x^2-10x-15\ \textless \ 0\\\\\frac{D}{4}=25+15=40\; ,\; x_{1,2}= 5\pm \sqrt{40}=5\pm 2\sqrt{10}\\\\x_1=5-2\sqrt{10}\approx -1,3\\\\x_2=5+2\sqrt{10}\approx 11,3\\\\x\in (5-2\sqrt{10}\, ;\, 5+2\sqrt{10})\\\\Celue\; x\; :\; \; -1;\; 0;\; 1;\; 2;\; 3;\; 4;\; 5;\; 6;\; 7;\; 8;\; 9;\; 10;\; 11\; .\\\\Otvet:\; \; 13.$