Question

Решите неравенства: a)t(t-1)< 0; б)t(t-1/4)(t-12)\geq=0; в)x^2-x> 0 г)2x+x^1\leq=0.

Answer 1

$1)\quad t(t-1)\ \textless \ 0\\\\+++(0)---(1)+++\\\\x\in (0,1)\\\\2)\quad t(t-\frac{1}{4})(t-12) \geq 0\\\\---[0]+++[\frac{1}{4}]---[12]+++\\\\x\in [\, 0,\frac{1}{4}\, ]\cup [12,+\infty )\\\\3)\quad x^2-x\ \textgreater \ 0\\\\x(x-1)\ \textgreater \ 0\\\\+++(0)---(1)+++\\\\x\in (-\infty ,0)\cup (1,+\infty )\\\\4)\quad 2x+x^2 \leq 0\\\\x(2+x) \leq 0\\\\+++[-2\, ]---[\, 0\, ]+++\\\\x\in [-2,0\, ]$