Odpowiedź:
x - mianownik
[tex] \frac{x + 1}{x} [/tex]
[tex] \frac{x + 1}{x} - 0.2 \times \frac{x}{x + 1} = 1.09[/tex]
[tex] \frac{x + 1}{x} - \frac{x}{5x + 5} = 1.09[/tex]
[tex] \frac{(x + 1)(5x + 5) - {x}^{2} }{x(5x + 5)} = 1.09[/tex]
[tex] \frac{5 {x}^{2} + 10x + 5 - {x}^{2} }{5 {x}^{2} + 5x } = \frac{109}{100} [/tex]
[tex] \frac{4 {x}^{2} + 10x + 5}{5 {x}^{2} + 5x} = \frac{109}{100} [/tex]
[tex]400 {x}^{2} + 1000x + 500 = 545 {x}^{2} + 545x[/tex]
[tex]145 {x}^{2} - 455x - 500 = 0[/tex]
[tex]29 {x}^{2} - 91x - 100 = 0[/tex]
Δ = 8281 + 11600 = 19881
[tex]x_{1} = \frac{91 - 141}{58} = - \frac{50}{58} = - \frac{25}{29} [/tex]
[tex]x_{2} = \frac{91 + 141}{58} = \frac{232}{58} = 4[/tex]
z racji że ułamek jest dodatni to pierwsza odpowiedź odpada
[tex]szukanym \: ułamkiem \: jest \: \frac{5}{4} [/tex]
