[tex]a)\\\\ x^3+2x^2+x=0\\\\x( x^2+2x+1)=0 \\\\x(x+1)^2=0\\\\x=0\ \ lub\ \ x+1=0\\\\x=0\ \ lub\ \ x=-1[/tex]
[tex]b)\\\\ (x^2-1)(x^2+25)+10x(x^2-1)=0\\\\ (x^2-1)(x^2 +10x +25)=0\\\\(x-1)(x+1)(x+5)^2=0\\\\x-1=0\ \ lub\ \ \ x+1=0\ \ lub\ \ x+5=0\\\\x=1\ \ lub\ \ x=-1\ \ lub\ \ \ x=-5[/tex]
[tex]c)\\\\ \frac{x-3}{2x-6}=2\\\\2x-6\neq 0\\2x\neq 6\ \ |:2\\x\neq 3 \\D=R\setminus \left \{ 3 \right \}\\\\ \frac{x-3}{2(x-3)}=2\\\\\frac{1}{2}=2\\\\sprzeczne, brak\ rozwiazania[/tex]
[tex]d)\\\\ \frac{8 }{ x-1}= \frac{x+5}{x}\\\\x-1\neq 0\ \ i\ \ x\neq 0 \\x\neq 1\ \ i\ \ x\neq 0\\\\D=R\setminus \left \{ 0,1 \right \}[/tex]
[tex](x+5)(x-1) =8x\\\\x^2-x+5x-5-8x=0\\\\x^2-4x-5=0\\a=1,\ \ b=-4,\ \ c=-5 \\\\\Delta =b^2-4ac=(-4)^2-4*1*(-5)=16+20=36\\\\\sqrt{\Delta }=\sqrt{36}=6\\\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{4-6}{2*1}=\frac{-2}{2}=-1\\\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{4+6}{2*1}=\frac{10}{2}=5[/tex]
