2.
[tex]3(x-2)^2=9(x-2)\\\\3(x^2-4x+4)=9x-18\\\\3x^2-12x+12-9x+18=0\\\\3x^2-21x+30=0\\\\x^2-7x+10=0\\\\\Delta=9\rightarrow \sqrt{\Delta}=3\\\\x_1=\frac{7-3}{2}\ \vee \ x_2=\frac{7+3}{2}\\\\x_1=2\ \vee \ x_2=5\\[/tex]
[tex](x+3)^2=4(x-1)^2\\\\x^2+6x+9=4(x^2-2x+1)\\\\x^2+6x+9=4x^2-8x+4\\\\-3x^2+14x+5=0\\\\\Delta=256\rightarrow \sqrt{\Delta}=16\\\\x_1=\frac{-14-16}{-6}\ \vee \ x_2=\frac{-14+16}{-6}\\\\x_1=5\ \vee \ x_2=-\frac{1}{3}\\[/tex]
3.
[tex]5x+2 > \frac{6x-x^2}{2}|*2\\\\10x+4 > 6x-x^2\\\\x^2+4x+4 > 0\\\\(x+2)^2 > 0\\\\(x+2)^2=0\\\\x=-2\\\\x\in R\setminus\{-2\}\\[/tex]
4.
[tex]w(x)=4x^3+4x^2-13x+5\\\\w(x)=4x^3+8x^2-5x-4x^2-8x+5\\\\w(x)=x(4x^2+8x-5)-1(4x^2+8x-5)\\\\w(x)=(x-1)(4x^2+8x-5)\\\\w(x)=(x-1)(4x^2-2x+10x-5)\\\\w(x)=(x-1)[2x(2x-1)+5(2x-1)]\\\\w(x)=(x-1)(2x-1)(2x+5)\\[/tex]
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2.
[tex]3(x-2)^2=9(x-2)\\\\3(x^2-4x+4)=9x-18\\\\3x^2-12x+12-9x+18=0\\\\3x^2-21x+30=0\\\\x^2-7x+10=0\\\\\Delta=9\rightarrow \sqrt{\Delta}=3\\\\x_1=\frac{7-3}{2}\ \vee \ x_2=\frac{7+3}{2}\\\\x_1=2\ \vee \ x_2=5\\[/tex]
[tex](x+3)^2=4(x-1)^2\\\\x^2+6x+9=4(x^2-2x+1)\\\\x^2+6x+9=4x^2-8x+4\\\\-3x^2+14x+5=0\\\\\Delta=256\rightarrow \sqrt{\Delta}=16\\\\x_1=\frac{-14-16}{-6}\ \vee \ x_2=\frac{-14+16}{-6}\\\\x_1=5\ \vee \ x_2=-\frac{1}{3}\\[/tex]
3.
[tex]5x+2 > \frac{6x-x^2}{2}|*2\\\\10x+4 > 6x-x^2\\\\x^2+4x+4 > 0\\\\(x+2)^2 > 0\\\\(x+2)^2=0\\\\x=-2\\\\x\in R\setminus\{-2\}\\[/tex]
4.
[tex]w(x)=4x^3+4x^2-13x+5\\\\w(x)=4x^3+8x^2-5x-4x^2-8x+5\\\\w(x)=x(4x^2+8x-5)-1(4x^2+8x-5)\\\\w(x)=(x-1)(4x^2+8x-5)\\\\w(x)=(x-1)(4x^2-2x+10x-5)\\\\w(x)=(x-1)[2x(2x-1)+5(2x-1)]\\\\w(x)=(x-1)(2x-1)(2x+5)\\[/tex]