Question

Aratati ca nr c=(2 la puterea 40+ 2 la puterea 39+2 la puterea 38):7 este patrat perfect
Va rog ajutati-ma

Answer 1

$c=(2^{40}+2^{39}+2^{38}):7 \\\\ c=2^{38}(2^2+2+1):7 \\\\ c=2^{38}(4+3):7 \\\\c=2^{38}*7:7 \\\\ c=2^{38} \\\\ c= (2^{19})^2 -este \ p.p.$

Answer 2

(2⁴⁰+2³⁹+2³⁸):7=
2³⁸(2²+2¹+2°):7=
2³⁸x7:7=2³⁸=(2¹⁹)²  deci patrat perfect