Răspuns:
n = 256
Explicație pas cu pas:
[tex]\frac{81^{2n+2}+3^{8n+7} -3^{8n+5} }{27^{685} -9^{1027}-3^{2053} } =\\ \\ =\frac{3^{4(2n+2)}+3^{8n+7} -3^{8n+5} }{3^{2055} -3^{2054}-3^{2053} } =\\ \\ =\frac{3^{8n+8}+3^{8n+7} -3^{8n+5} }{3^{2055} -3^{2054}-3^{2053} }=\\ \\ =\frac{3^{8n+5} 3^{3}+3^{8n+5}3^{2}-3^{8n+5}}{3^{2053}(3^{2} -3-1) } =\\ \\ \frac{3^{8n+5}(27+9-1)}{3^{2053} 5} =\\ \\= \frac{3^{8n+5}35}{3^{2053} 5}=\\ \\ = \frac{3^{8n+5}7}{3^{2053} }=[/tex]
8n + 5 = 2053
8n = 2048
n = 256
... și-mi datorezi o pereche de ochelari :)
