[latex]f(x)=sqrt{3-x}-3sqrt{x+1}\ 3-xgeq0 wedge x+1geq0\ xleq3 wedge xgeq -1\ oxed{D=xin langle -1;3 angle}\ f(x_0)=0\ 0=sqrt{3-x}-3sqrt{x+1}\ 3sqrt{x+1}=sqrt{3-x}|()^2\ 9(x+1)=3-x\ 9x+9=3-x\ 10x=-6\ oxed{x=frac{-6}{10}in D} [/latex] [latex]f(x)=frac{x}{sqrt{x^2-4sqrt{2}+8}}-frac{1}{2sqrt{2}}\ Jedynym zastrzezeniem jest:\ x^2-4sqrt{2}+8>0 nie badz rowne, bo nie mozna dzielic przez 0\ Mamy tutaj nierownosc kwadratowa\ Delta =(4sqrt{2})^2-4*1*8=0\ x=frac{-(-4sqrt{2})}{2*1}=2sqrt{2}\ Parabola jest wesola wiec i Delta =0 wiec znajduje sie nad osia OX\ i ma jeden punkt styku z osia OX wiec zbior rozwiazan tej\ nierownosci to:\[/latex] [latex]xin (-infty;2sqrt{2})cup(2sqrt{2};+infty), inaczej:\ oxed{xin Resetminuslbrace2sqrt{2} brace}\ f(x_0)=0\ 0=frac{x}{sqrt{x^2-4sqrt{2}x+8}}-frac{1}{2sqrt{2}}\ frac{1}{2sqrt{2}}=frac{x}{sqrt{x^2-4sqrt{2}x+8}}|()^2\ frac{1}{8}=frac{x^2}{x^2-4sqrt{2}x+8}\ x^2-4sqrt{2}x+8=8x^2\ -7x^2-4sqrt{2}+8=0\ Delta=(-4sqrt{2})^2-4*(-7)*8=256\ sqrt{Delta}=sqrt{256}=16\[/latex] [latex]x_1=frac{-(-4sqrt{2})+16}{2*(-7)}=frac{4sqrt{2}+16}{-7*2}=underline{-frac{2}{7}sqrt{2}-frac{8}{7}}\ x_2=frac{4sqrt{2}-16}{-7*2}=underline{-frac{2}{7}sqrt{2}+frac{8}{7}}\ x_1,x_2in D, wiec:\ oxed{x_0in lbrace-frac{2}{7}sqrt{2}-frac{8}{7};-frac{2}{7}sqrt{2}+frac{8}{7}}}[/latex]
