[latex]a)\ 5x^2-4x-1=0\ Delta=36, sqrt{Delta} =6\ x_{1} =1\ x_{2} = - frac{1}{5} [/latex] [latex]b)\ 9x^2+12x=-4\ 9x^2+12x+4=0\ Delta= 1, sqrt{Delta}=1\ x_{1} = -frac{11}{18} x_{2} = -frac{13}{18} \ [/latex] [latex]c)\ 3x^2-2x-5=6x-x^2\ 3x^2-2x-5-6x+x^2=0\ 4x^2-8x-5=0\ Delta= 144, sqrt{Delta}=12\ x_{1} = frac{5}{2}, x_{2} =- frac{1}{2} [/latex] [latex]d) x-4x^3+4x^2=1\ -4x^3+4x^2+x-1=0\ -4x^2(x-1)+1(x-1)=0\ (x-1)(-4x^2+1)=0\ x=1 x= frac{1}{2},x= -frac{1}{2}[/latex]
[latex]Delta=b^{2}-4ac\ x_{1}=frac{-x-sqrtDelta}{2a}\ x_{1}=frac{-x-sqrtDelta}{2a}\ ----------\ 5x^{2}-4x-1=0\ Delta=(-4)^{2}-4*5*(-1)=16+20=36\ sqrt{Delta}=6\ x_{1}=frac{4-6}{10}=frac{-2}{10}=-frac{1}{5}\ x_{2}=frac{4+6}{10}=frac{10}{10}=1\ ----------\ 9x^{2}+12x=-4\ 9x^{2}+12x+4=0\ (3x)^{2}+2*3x*2+2^{2}=0\ (3x+2)=0\ 3x+2=0\ 3x=-2\ x=-frac{2}{3} - pierwiastek dwukrotny\ ----------\[/latex] [latex]3x^{2}-2x-5=6x-x^{2}\ 4x^{2}-8x-5=0\ Delta=(-8)^{2}-4*4*(-5)=64+80=144\ sqrt{Delta}=12\ x_{1}=frac{8-12}{8}=frac{-4}{8}=-frac{1}{2}\ x_{2}=frac{8+12}{8}=frac{20}{8}=frac{5}{2}\ ----------\ x-4x^{3}+4x^{2}=1\ -4x^{3}+4x^{2}+x-1=0\ -4x^{2}(x-1)+(x-1)=0\ (x-1)(1-4x)=0\ 4(x-1)(frac{1}{4}-x)=0\ 4(x-1)(frac{1}{2}-x)(frac{1}{2}+x)=0\ x=1 vee x=frac{1}{2} vee x=-frac{1}{2}[/latex]
