2.
[tex]a) \\(x+1)(x-1)+(x+2)(x-2)-(x+3)(x-3)=\\x^2-1^2+x^2-2^2-(x^2-3^2)=\\x^2-1+x^2-4-(x^2-9)=\\x^2-1+x^2-4-x^2+9=\\x^2+4\\\\x^2+4 \text{ dla } x = \sqrt{3}\\(\sqrt3)^2+4=3+4=7[/tex]
[tex]b) \\(1-2x)(1+2x)+(1-3x)(1+3x)-(1-4x)(4x+1)=\\1^2-(2x)^2+1^2-(3x)^2-(1-4x)(1+4x)=\\1-4x^2+1-9x^2-(1-(4x)^2)=\\1-4x^2+1-9x^2-1+16x^2=\\1+3x^2\\\\1+3x^2 \text{ dla } x = \sqrt5\\1+3*(\sqrt5)^2=1+3*5=1+15=16[/tex]
[tex]c) \\(2x-1)^2-(2x-1)(1+2x)-(2x+1)^2=\\(2x)^2-2*2x*1+1^2-(2x-1)(2x+1)-((2x)^2+2*2x*1+1^2)=\\4x^2-4x+1-((2x)^2-1^2)-(4x^2+4x+1)=\\4x^2-4x+1-4x^2+1-4x^2-4x-1=\\-4x^2-8x+1[/tex]
[tex]-4x^2-8x+1 \text{ dla } x=\sqrt2\\-4*(\sqrt2)^2-8*\sqrt2+1=-4*2-8\sqrt2+1=-8-8\sqrt2=1=-7-8\sqrt2[/tex]
