Question

помогите решить, пожалуйста. Номер 28 и 29

Answer 1

$1)\; \; y=-(x+1)^2+\sqrt2\; \; \; \Rightarrow \\\\x(vershinu)=-1\; ,\; y(vershinu)=\sqrt2\\\\y\in (-\infty ,\sqrt2\, ]\\\\2)\; \; \frac{2}{x+1}-\frac{1}{x-1}<1\; ,\; \; ODZ:\; \; x\ne -1\; ,\; x\ne 1\\\\\frac{2(x-1)-(x+1)-(x+1)(x-1)}{(x+1)(x-1)}<0\\\\\frac{2x-2-x-1-x^2+1}{(x+1)(x-1)}<0\\\\\frac{-(x^2-x+2)}{(x+1)(x-1)}<0\; \; \to\; \; \frac{x^2-x+2}{(x+1)(x-1)}>0\\\\x^2-x+2=0\; ,\; \; D=1-4\cdot 2<0\; \; \to \; \; x^2-x+2>0\; pri\; x\in R\\\\\frac{x^2-x+2}{(x+1)(x-1)}>0\; \; \to \; \; (x+1)(x-1)>0\; \; \to \\\\x\in (-\infty ,-1)\cup (1,+\infty )$