Odpowiedź:
Szczegółowe wyjaśnienie:
a)
100[tex]x^{2} \\[/tex]-81=0
100[tex]x^{2}[/tex]= 81 /:100
[tex]x^{2}[/tex]=[tex]\frac{81}{100}[/tex]
x= [tex]\sqrt{\frac{81}{100} }[/tex]
[tex]x_{1}[/tex]= [tex]\frac{9}{10\\\frac}[/tex] v [tex]x_{2}[/tex]= -[tex]\frac{9}{10}[/tex]
b)
[tex]\frac{1}{4} x^{2} - \frac{1}{9}=0 / *36\\9x^{2}-4=0\\9x^{2} =4 /:9\\x^{2} = \frac{4}{9} \\x_{1}= \frac{2}{3} v x_{2} = -\frac{2}{3}[/tex]
c)
[tex]x^{2} + 10 x +25 = 0 \\\\[/tex]
[tex](x+5)^{2}[/tex]=0
x+5=0
x=-5
d)
[tex]x^{2} +64 = 16x\\x^{2} +64-16x=0\\\\>>>> a^{2} - 2ab+b^{2} = (a-b)^{2} \\(x-8)^{2} =0\\x-8=0\\x= 8[/tex]
e)
[tex]24x-x^{2} =144\\24x-x^{2} -144=0\\-(x^{2} -24x+144) = 0 \\-(x-12)^{2} =0\\x-12=0\\x=12[/tex]
f)
[tex]1+9x^{2} +6x=0\\9x^{2} +6x+1 = 0\\(3x+1)^{2}=0\\3x+1=0\\3x=-1 / :3\\x=-\frac{1}{3}[/tex]
