[tex]a)\\\\x^2+1=5-2x^2\\x^2+2x^2=5-1\\3x^2=4 /:3\\x^2=\frac43\\x=\sqrt{\frac43}=\frac{2}{\sqrt3}=\frac{2\sqrt3}3 \text{ v } -\frac{2\sqrt3}3\\x=\frac{2\sqrt3}3 \text{ lub } x = -\frac{2\sqrt3}3[/tex]
[tex]b)\\\\3(x^2+1)=5 /:3\\x^2+1=\frac53 /-\frac33\\x^2=\frac23\\x=\sqrt{\frac23}=\frac{\sqrt2}{\sqrt3}=\frac{\sqrt6}3 \text{ v } -\frac{\sqrt6}3\\x=\frac{\sqrt6}3 \text{ lub } x=-\frac{\sqrt6}3[/tex]
[tex]c)\\\\(x-1)^2=-2x\\x^2-2x+1=-2x\\x^2+1=0\\x^2=-1\\x \neq \sqrt{-1}\\\text{Brak rozwiazan}[/tex]
[tex]d) \\\\(\frac12x-1)(\frac12x+1)=2\\(\frac12x)^2-1^1=2\\\frac14x^2-1=2 /+1\\\frac14x^2=3 /*4\\x^2=12\\x=\sqrt{12}=\sqrt{4*3}=2\sqrt3 \text{ v } -2\sqrt3\\x=2\sqrt3 \text{ lub } x=-2\sqrt3[/tex]
[tex]e)\\\\(x+1)^2=(1-2x)^2\\x^2+2x+1=1-4x+4x^2\\x^2-4x^2+2x+4x+1-1=0\\-3x^2+6x=0\\\Delta=6^2-4*(-3)*0=36\\\sqrt{\Delta}=6\\x_1=\frac{-6-6}{-6}=\frac{-12}{-6}=2\\x_2=\frac{-6+6}{-6}=0[/tex]
[tex]f)\\\\(3x-2)^2=(2x+3)^2\\9x^2-12x+4=4x^2+12x+9\\9x^2-4x^2-12x-12x+4-9=0\\5x^2-24x-5=0\\\Delta=(-24)^2-4*5*(-5)=576+100=676\\\sqrt{\Delta}=26\\x_1=\frac{24-26}{10}=\frac{-2}{10}=-\frac15\\x_2=\frac{24+26}{10}=\frac{50}{10}=5[/tex]
