Question

Aratati ca numarul n=27^9•32^11:2-16^6•2•6^27 este patrat perfect

Answer 1

n = (3^3)^9 x (2^5)^11 :2 - (2^4)^6 x 2 x (2x3)^27 = 3^27 x 2^55:2 - 2^24 x 2 x 2^27 x 3^27 = 3^27 x 2^54 - 2^52 x 3^27 = 2^52 x 3^27 (2^2 - 1) = 2^52 x 3^27 x 3 = 2^52 x 3^28 = (2^26 x 3^14)^2, deci este patrat perfect