Question

aratati ca nr a=(3la puterea21+3la puterea26+3la puterea19):39este patrat perfect

Answer 1

3^21 +3^26 +3^19 =3^19(3^2 +3^7+1) =3^19 (9+2187+1)
=3^19 x2197
(3^19x2197) :39 =3^19 x169:3= 3^18x(13)^2
a=[3^9]^2x13^2 =(13x3^9)^2  deci este patrat perfect

Answer 2

a=($3^{19}$+$3^{20}$+$3^{21}$):39
a=$3^{19}$(1+3+$3^{2}$):39
a=$3^{19}$×13:39
a=$3^{19}$×$\frac{1}{3}$
a=$\frac{3^{19} }{3}$
a=$3^{18}$=($3^{9}$)²