[tex] x+ \dfrac{1}{x} = 2 \Big|^3 \\ \\ x^3 + 2\cdot x^2 \cdot \dfrac{1}{x} + 2\cdot x\cdot \Big(\dfrac{1}{x}\Big)^2 + \Big(\dfrac{1}{x}\Big)^3 = 2^3 \\ \\x^3 + 2\cdot x^2 \cdot \dfrac{1}{x} + 2\cdot x\cdot \dfrac{1}{x^2} +\dfrac{1}{x^3} = 8\\ \\ x^3 + \dfrac{1}{x^3} + 2\cdot x + 2\cdot \dfrac{1}{x} = 8 \\ \\ x^3 + \dfrac{1}{x^3} + 2\cdot\Big( x + \dfrac{1}{x} \Big) = 8 \\ \\ x^3 + \dfrac{1}{x^3} + 2\cdot2 = 8 \\ \\ x^3 + \dfrac{1}{x^3} = 8- 4 \\ \\ x^3 + \dfrac{1}{x^3} = 4[/tex]
