1) х > 1
x
x - 1 >0
x
x²-1 >0
x
{x(x²-1)>0
{x≠0
x(x²-1)>0
x(x-1)(x+1)>0
x=0 x=1 x=-1
- + - +
------- -1 --------- 0 ----------- 1 ----------
\\\\\\\\\\\ \\\\\\\\\\\\\\\
x∈(-1; 0)∨(1; +∞)
2) x-3 >1
x+2
x-3 - 1 >0
x+2
x-3 -x-2 >0
x+2
- 5 >0
x+2
{-5(x+2)>0
{x+2≠0
{x+2<0<br>{x≠-2
{x<-2<br>{x≠-2
\\\\\\\\\\
--------- -2 ----------------------
x∈(-∞; -2)
3) 2x⁴+3x²-5<0<br>Пусть у=х²
2у²+3у-5<0<br>Парабола, ветви вверх.
2у²+3у-5=0
Д=9+4*2*5=9+40=49
у₁=-3-7=-2,5
4
у₂=-3+7=1
4
+ - +
------- -2,5 --------- 1 -----------
\\\\\\\\\\\\
-2,5<у<1<br>-2.5
{x²>-2.5
{x²<1<br>
x²>-2.5
верно при любых х.
х²<1<br>x²-1<0<br>(x-1)(x+1)<0<br>x=1 x=-1
+ - +
------- -1 --------- 1 ---------
\\\\\\\\\\\
x∈(-1; 1)