Odpowiedź:
2
a)
[tex](x-5)x(x+5)=x^{2} -100x\\x^{2} -25=x^{2} -100x\\-25=-100x\\-100x=-25\\x=\frac{1}{4}[/tex]
b)
[tex](3-x)^{2}-(x+\frac{1}{3})^{2}=\frac{2}{9}\\ 9-6x+x^{2} -(x^{2} +\frac{2}{3}x+\frac{1}{9})=\frac{2}{9}\\ 9-6x+x^{2} -x^{2} -\frac{2}{3}x-\frac{1}{9}=\frac{2}{9}\\ \frac{80}{9}-\frac{20}{3}x=\frac{2}{9}\\ 80-60x=2\\ -60x=2-80\\ -60x=-78\\ x=\frac{13}{10}[/tex]
c)
[tex]4(\frac{1}{2}x-3)^{2}=(6-x)^{2}\\ 4(\frac{1}{4}x^{2} -3x+9)=36-12x+x^{2} \\ x^{2} -12x+36=36-12x+x^{2} \\[/tex]
e)
[tex](6+\frac{1}{3}x)x(-\frac{1}{3} x+6)+(\frac{1}{3}x-4)^{2}=4\\ (6+\frac{1}{3}x)x(6-\frac{1}{3}x)+\frac{1}{9}x^{2} -\frac{8}{3}x+16=4\\ 36-\frac{1}{9}x^{2} +\frac{1}{4}x^{2} -\frac{8}{3}x+16=4\\ 52-\frac{8}{3} x=4\\ 156-8x=12\\ -8x=12-156\\ -8x=-144\\ x=18[/tex]
Szczegółowe wyjaśnienie:
