Question

Demonstrati ca numarul $4^{2n} + 2^{2n+1} + 1$ , n∈N,este patrat perfect

Answer 1

4^2n+2^(2n+1)+1 = (2^2n+1)²
patratul perfect este de forma (a+b)²=a²+2ab+b²
a²=4^2n=(2^2n)²
b²=1=1²
2ab= 2x(2^2n)x1=2^(2n+1)