a) [latex](sqrt{3}y+2)^2-(sqrt{3}y+2)(sqrt{3}y-2)=0[/latex] [latex]3y^2+4 sqrt{3}y+4-(3y^2-4)=0[/latex] [latex]3y^2+4 sqrt{3}y+4-3y^2+4=0[/latex] [latex]4 sqrt{3}y=-4-4[/latex] [latex]4 sqrt{3}y=-8 /:4 sqrt{3}[/latex] [latex]y=- frac{8}{4 sqrt{3}}[/latex] [latex]y=- frac{2}{sqrt{3}}[/latex] b) [latex]frac{5x^2+2}{5}=(x-3)^2[/latex] [latex]frac{5x^2+2}{5}=x^2-6x+9 /cdot 5[/latex] [latex]5x^2+2=5x^2-30x+45[/latex] [latex]5x^2-5x^2+30x=45-2[/latex] [latex]30x=43 /:30[/latex] [latex]x=1 frac{13}{30}[/latex] c) [latex]frac{(2x- sqrt{2} )(2x+sqrt{2})}{2} - frac{ 6(x-1)^2}{3}=0[/latex] [latex]frac{4x^2-2}{2} - 2(x-1)^2=0[/latex] [latex]frac{2(2x^2-1)}{2} - 2(x^2-2x+1)=0[/latex] [latex]2x^2-1- 2x^2+4x-2=0[/latex] [latex]2x^2- 2x^2+4x=1+2[/latex] [latex]4x=3 /:4[/latex] [latex]x= frac{3}{4}[/latex] d) [latex]frac{(2y-2)^2}{4}= frac{(3y+1)^2}{9} /cdot 36[/latex] [latex]9(4y^2-8y+4)=4(9y^2+6y+1)[/latex] [latex]36y^2-72y+36=36y^2+24y+4[/latex] [latex]36y^2-72y-36y^2-24y=4-36[/latex] [latex]-72y-24y=4-36[/latex] [latex]- 96y=-32 /:(-96)[/latex] [latex]y= frac{1}{3} [/latex]
