7. si x 1 234frac5167x8910 11 512 calcula E 13 1415x162 17 18frac1912021x222232425

Apuntes

To solve the equation \(x + \frac{1}{x} = 5\) and calculate \(E = x^2 + \frac{1}{x^2}\), we can use the following steps: First, we can square both sides of the equation \(x + \frac{1}{x} = 5\): \[ \left(x + \frac{1}{x}\right)^2 = 5^2 \] This expands to: \[ x^2 + 2 + \frac{1}{x^2} = 25 \] Now, we can rearrange this equation to isolate \(x^2 + \frac{1}{x^2}\): \[ x^2 + \frac{1}{x^2} = 25 - 2 \] Thus, we have: \[ x^2 + \frac{1}{x^2} = 23 \] Now, we can conclude that: \[ E = x^2 + \frac{1}{x^2} = 23 \] Therefore, the answer is: **a) 23**