1.Rozwiąż podane równanie,nierówności (x-1)²/2-(x+2)(x-2)≤(x+2)²/2= /-kreska ułamkowa

[latex]frac{(x-1)^{2}}{2}-(x+2)(x-2) leq frac{(x+2)^2}{2} /*2 \ \(x-1)^{2}-2(x^2-4) leq (x+2)^2 \ \x^2-2x+1-2x^2+8 leq x^2+4x+4\ \x^2-2x+1-2x^2+8- x^2-4x-4leq 0 \ \-2x^2 -6x +5 leq 0[/latex] [latex]miejsca zerowe \ \ Delta = b^{2}-4ac = (-6)^{2}-4* (-2)*5=36+40=76\ \sqrt{Delta }=sqrt{76}=sqrt{4*19}=2sqrt{19}\ \x_{1}=frac{-b-sqrt{Delta }}{2a} =frac{6-2sqrt{19}}{-4}= frac{-2 ( sqrt{19}-3)}{-4}= frac{ sqrt{19}-3 }{2}[/latex] [latex]x_{2}=frac{-b+sqrt{Delta }}{2a} =frac{6+2sqrt{19}}{-4}= frac{ 2 ( 3 +sqrt{19} )}{-4}=frac{ 3 +sqrt{19 }}{-2} =frac{ -3 -sqrt{19 }}{ 2} \ \ a <0 ramiona paraboli skierowane sa w dol \ \x in (-infty ,frac{ -3 -sqrt{19 }}{ 2} > cup