Question

aratati ca numarul
N = 2 la 2n + 2 la 2n + 3 + 2 la 2n + 4 este un patrat perfect
Va rog dau coroana


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Answer 1

 

$\displaystyle\bf\\N = 2^{2n} + 2^{2n+3} + 2^{2n+4}\\\\N = 2^{2n} + 2^{2n}\times2^3 + 2^{2n}\times2^4\\\\\textbf{Dam factor comun pe }~2^{2n}\\\\N=2^{2n}(1+2^3+2^4)\\\\N=2^{2n}(1+8+16)\\\\N=2^{2n} \times25\\\\N=\Big(2^{n}\Big)^2 \times5^2\\\\\boxed{\bf~N=\Big(2^{n}\times5\Big)^2=pp}$