Odpowiedź:
[tex]1)\\\\100x^2-81=0\\\\(10x-9)(10x+9)=0\\\\10x-9=0\ \ \ \ \ \ \vee\ \ \ \ 10x+9=0\\\\10x=9\ \ /:10\ \ \ \ \vee\ \ \ \ 10x=-9\ \ /:10\\\\x=\frac{9}{10}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=-\frac{9}{10}[/tex]
[tex]2)\\\\\frac{1}{4}x^2-\frac{1}{9}=0\ \ /*36\\\\9x^2-4=0\\\\(3x-2)(3x+2)=0\\\\3x-2=0\ \ \ \ \ \ \vee\ \ \ \ 3x+2=0\\\\3x=2\ \ /:3\ \ \ \ \vee\ \ \ \ 3x=-2\ \ /:3\\\\x=\frac{2}{3}\ \ \ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=-\frac{2}{3}[/tex]
[tex]3)\\\\4x^2-x-5=0\\\\\Delta=b^2-4ac=(-1)^2-4*4*(-5)=1+80=81\\\\\sqrt{\Delta}=\sqrt{81}=9\\\\\\x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*4}=\frac{1-9}{8}=\frac{-8}{8}=-1\\\\\\x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*4}=\frac{1+9}{8}=\frac{10}{8}=\frac{5}{4}=1\frac{1}{4}[/tex]
[tex]4)\\\\3x^2-5x-2=0\\\\\Delta=b^2-4ac=(-5)^2-4*3*(-2)=25+24=49\\\\\sqrt{\Delta}=\sqrt{49}=7\\\\\\x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*3}=\frac{5-7}{6}=\frac{-2}{6}=-\frac{1}{3}\\\\\\x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*3}=\frac{5+7}{6}=\frac{12}{6}=2[/tex]