Question

Fie x numar real nenul.
Calculati x la a 4a + 1/x la a patra in functie de a=x+1/x.

Answer 1

Răspuns:

Explicație pas cu pas:

(x + 1/x)^2 = x^2 + 2x*1/x + 1/x^2 = x^2 + 1/x^2 + 2

x^2 + 1/x^2 = (x + 1/x)^2 - 2 = a^2 - 2

(x^2 + 1/x^2)^2 = x^4 + 2 + 1/x^4

x^4 + 1/x^4 = (x^2 + 1/x^2)^2 - 2 = ( a^2 - 2)^2 - 2 = a^4 - 4a^2 + 4 - 2 = a^4 - 4a^2 + 2