x- 1 supra x =3
Calculati : x la patrat +1 supra x la patrat
Si x la puterea a 3 a +1 supra x la puterea a 3 a

[tex] \frac{x - 1}{x} = 3[/tex]

[tex]3x = x - 1[/tex]

[tex]3x - x = - 1[/tex]

[tex]2x = - 1[/tex]

[tex]x = - \frac{1}{2} [/tex]

[tex] {x}^{2} + \frac{1}{ {x}^{2} } = {( - \frac{1}{2}) }^{2} + \frac{1}{{( - \frac{1}{2}) }^{2}} = \frac{1}{4} + \frac{1}{ \frac{1}{4} } = \frac{1}{4} + 4 = \frac{1}{4} + \frac{16}{4} = \frac{16 + 1}{4} = \frac{17}{4} [/tex]

[tex] {x}^{3} + \frac{1}{ {x}^{3} } = {( - \frac{1}{2} )}^{3} + \frac{1}{{( - \frac{1}{2} )}^{3} } = - \frac{ 1}{8} - \frac{1}{ \frac{1}{8} } = - \frac{1}{8} - 8 = - \frac{1}{8} - \frac{64}{8} = \frac{ - 1 - 64}{8} = - \frac{ 65}{8} [/tex]