Question

Dacă 4^n +4^-n= 4, atunci 16^n +16^-n egal cu cat?

Answer 1

Răspuns:

Explicație pas cu pas:

4^-n = 1/4^n

4^n + 1/4^n = 4

Ridicam la patrat

(4^n + 1/4^n)^2 = 16

4^2n + 1/4^2n + 2*4^n/4^n = 16

4^2n = (4^2)^n = 16^n

16^n + 1/16^n + 2 = 16

16^n + 1/16^n = 16 - 2 = 14

Answer 2

$4^n+4^{-n} = 4 \Big|^2 \\ \\ (4^{n})^2+2\cdot 4^n\cdot 4^{-n}+(4^{-n})^2 = 16 \\ \\ 4^{2n}+2+4^{-2n} = 16 \\ \\ {(4^2)}^n+{(4^{2})}^{-n} = 16-2 \\ \\ \Rightarrow \boxed{16^n+16^{-n} = 14}$