Rozwiąż równanie a) [latex] frac{x(3x+2)}{x-4}=x-1, x eq 4 [/latex] b)[latex] x^{3} - 7x^{2} +6x=0 [/latex]

[latex] frac{x(3x+2)}{x-4}=x-1 /*(x-4) x eq 4 \ \ 3x^2+2x=x^2-4x-x+4\ 3x^2+2x=x^2-5x+4\ 2x^2+7x-4=0\ \ Delta=49+32=81\ sqrt{Delta}=sqrt{81}=9\ \ x_1=frac{-7-9}{4}=-frac{16}{4}=-4\ \ x_2=frac{-7+9}{4}=frac{1}{2}\ \ oxed{xin{-4;frac{1}{2}}}[/latex] [latex] x^{3} - 7x^{2} +6x=0 \ x(x^2-7x+6)=0\ x(x-1)(x-6)=0\ x_1=0 vee x_2=1 vee x_3=6\ \ oxed{xin{0,1,6}}[/latex]

[latex] a) quadfrac{x(3x+2)}{x-4}=x-1, x eq 4 \ \ \ frac{3x^2+2x}{x-4}=(x-1) \ \ 3x^2+2x=(x-1)(x-4)\ \ 3x^2+2x=x^2-4x-1x+4 \ \ 3x^2+2x-x^2+4x+1x-4=0 \ \ 2x^2+7x-4 = 0 o frac{-bpm sqrt{b^2-4ac}}{2a} qquad a=2quad b=7quad c=-4\ \ frac{-7pm sqrt{7^2-4(2)(-4)}}{2(2)}= frac{-7pm sqrt{49+32}}{4}=frac{-7pm sqrt{81}}{4}=\ \ star x_1=frac{-7+9}{4} o x_1= frac{2}{4} o oxed{x_1= frac{1}{2} } \ \ star x_2=frac{-7-9}{4} o x_2=frac{-16}{4} o oxed{x_2=-4} [/latex] [latex]b) quad x^{3} - 7x^{2} +6x=0 \ \ x(x^2-7x+6)=0 o oxed{x_1=0} \ \ (x^2-7x+6)=0 o frac{-bpm sqrt{b^2-4ac}}{2a} qquad a=1quad b=-7quad c=6\ \ x_{(2 y 3)} frac{7pm sqrt{(-7)^2-4(1)(6)}}{2(1)} \ \ frac{7pm sqrt{49-24}}{2} o frac{7pm sqrt{25}}{2} ofrac{7pm 5}{2} \ \ star x_2= frac{7+5}{2} o x_2= frac{12}{2} o oxed{x_2=6} \ \ star x_3= frac{7-5}{2} o x_3= frac{2}{2} o oxed{x_3=1} [/latex] pozdrowienia!!!!