Question

Se stie ca x+1/x=4(doar 1 este in fractie nu si x),unde x apartine R*.calculati:x la puterea a 4-a + 1/x la puterea a patra.(doar 1 este in fractie)
multumesc.

Answer 1

[tex]x+\frac{1}{x}=4\,\,|(...)^2\\ x^2+2\cdot{x}\cdot\frac{1}{x}+\frac{1}{x^2}=16\\ x^2+\frac{1}{x^2}=14\,\,|(...)^2\\ x^4+2\cdot{\not{x}^2}\cdot\frac{1}{\not{x}^2}+\frac{1}{x^4}=196\\ x^4+\frac{1}{x^4}=196-2=194.[/tex]