Question

a)(x+1)²+2>(x-3)²+2x
b)(x+1)(x+3)≤(X+5)²+2
c)(x-2)(x-1)≥(x+3)²+2
d)(x+1)²<x(x+3)+5
   ?????

Answer 1

1.
$x^2+2x+3>x^2-6x+9+2x\Rightarrow 6x>6\Rightarrow x>1\Rightarrow x\in(1;\infty)$

2.
$x^2+4x+3\leq x^2+10x+27\Rightarrow 6x\geq-24\Rightarrow x\geq-4\Rightarrow x\in[-4;\infty)$

3
$x^2-3x+2\geq x^2+6x+11\Rightarrow 9x\leq-9\Rightarrow x\leq-1\Rightarrow x\i(-\infty;-1]$

4.
$x^2+2x+1-4\Rightarrow x\in(-4;\infty)$^2+3x+5\rightarrow>