Odpowiedź:
[tex]a)\\\\9(x+2)(x-\frac{1}{2}x)=0\\\\(9x+18)\cdot\frac{1}{2}x=0\\\\\frac{9}{2}x^2+9x=0\ \ /\cdot2\\\\9x^2+18x=0\ \ /:9\\\\x^2+2x=0\\\\x(x+2)=0\\\\x=0\ \ \ \ \vee\ \ \ \ x+2=0\\\\x=0\ \ \ \ \vee\ \ \ \ x=-2[/tex]
[tex]b)\\\\x^2+2\sqrt{2}x+2=0\\\\(x+\sqrt{2})^2=0\\\\x+\sqrt{2}=0\\\\x=-\sqrt{2}\\\\\\c)\\\\5x^2-6x+7=0\\\\\Delta=b^2-4ac\\\\\Delta=(-6)^2-4\cdot5\cdot7=36-140=-104\\\\\Delta<0\ \ brak\ \ rozwiazania[/tex]
[tex]d)\\\\\frac{x+1}{2-x}=2x\\\\2-x\neq 0\\-x\neq -2\ \ /\cdot(-1)\\x\neq 2\\\\x+1=2x(2-x)\\\\x+1=4x-2x^2\\\\x+1-4x+2x^2=0\\\\2x^2-3x+1=0\\\\2x^2-x-2x+1=0\\\\x(2x-1)-(2x-1)=0\\\\(2x-1)(x-1)=0\\\\2x-1=0\ \ \ \ \vee\ \ \ \ x-1=0\\\\2x=1\ \ /:2\ \ \vee\ \ \ \ x=1\\\\x=\frac{1}{2}\ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=1[/tex]
[tex]f)\\\\x^3+2x^2-9x-18=0\\\\x^2(x+2)-9(x+2)=0\\\\(x+2)(x^2-9)=0\\\\(x+2)(x-3)(x+3)=0\\\\x+2=0\ \ \ \ \vee\ \ \ \ x-3=0\ \ \ \ \vee\ \ \ \ x+3=0\\\\x=-2\ \ \ \ \ \ \vee\ \ \ \ x=3\ \ \ \ \ \ \ \ \ \ \vee\ \ \ \x=-3[/tex]
[tex]g)\\\\\frac{x+2}{x-1}=3\\\\x-1\neq 0\\x\neq 1\\\\\\x+2=3(x-1)\\\\x+2=3x-3\\\\x-3x=-3-2\\\\-2x=-5\ \ /:(-2)\\\\x=\frac{5}{2}\\\\x=2\frac{1}{2}[/tex]
