Question

Aratati ca 9 la puterea n+1-3 la puterea 2n•5 este patrat perfect

Answer 1

$9^{n+1}-5\cdot 3^{2n}=9\cdot 9^n-5\cdot (3^2)^n=9\cdot 9^n-5\cdot 9^n=4\cdot 9^n=2^2\cdot 9^n=\\=2^2\cdot (3^2)^n=2^2\cdot (3^n)^2=(2\cdot 3^n)^2,\;care\;este\;p\check{a}trat\;perfect.$