Matematyka
pati06pol
2017-06-23 21:59:44
Oblicz: 1) x^2 = x + 2 2) f(x) = x^2 - 6x + 3
Odpowiedź
Ronnie16
2017-06-24 02:01:52

[latex]x^2 = x + 2\ x^2-x-2=0\ Delta=1-4cdot(-2)cdot 1 = 1+8=9\ sqrt{Delta}=sqrt{9}=3\ x_1=frac{1-3}{2}=frac{-2}{2}=-1\ x_2=frac{1+3}{2}=frac{4}{2}=2\ \ oxed{xin{-1;2}}[/latex] [latex]f(x) = x^2 - 6x + 3\ x^2-6x+3=0\ Delta=6^2-4cdot1cdot3=36-12=24\ sqrt{Delta}=sqrt{24}=sqrt{4cdot6}=2sqrt{6}\ \ x_1=frac{6-2sqrt{6}}{2}=3-sqrt{6}\ x_2=3+sqrt{6}\ \ oxed{f(x)=(x-3+sqrt{6})(x-3-sqrt{6})}[/latex]

rysiu1
2017-06-24 02:03:07

[latex]1)\x^2=x+2\x^2-x-2=0\\Delta=b^2-4ac\Delta=(-1)^2-4*1*(-2)=1+8=9\ sqrt{Delta}= sqrt{9} =3\\x_1= frac{-b- sqrt{Delta} }{2a}\x_1= frac{-(-1)-3}{2*1}= frac{1-3}{2}= frac{-2}{2} =-1\\x_2= frac{-b+ sqrt{Delta} }{2a}\x_2= frac{-(-1)+3}{2*1}= frac{1+3}{2}= frac{4}{2} =2[/latex] 2) [latex]f(x)=x^2-6x+3\x^2-6x+3=0\\Delta=b^2-4ac\Delta=(-6)^2-4*1*3=36-12=24\ sqrt{Delta}= sqrt{24} = sqrt{4*6}= sqrt{4} * sqrt{6} =2* sqrt{6}=2 sqrt{6} \\x_1= frac{-b- sqrt{Delta} }{2a}\x_1= frac{-(-6)-2 sqrt{6} }{2*1}= frac{6-2 sqrt{6} }{2}= frac{2(3- sqrt{6})}{2} =3- sqrt{6} \\x_2= frac{-b+ sqrt{Delta} }{2a} \x_2= frac{-(-6)+2 sqrt{6} }{2*1}= frac{6+2 sqrt{6} }{2}= frac{2(3+ sqrt{6})}{2} =3+ sqrt{6} [/latex]

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