Question

Aratati ca urmatoarele numere sunt pătrate perfecte:
a) 2^83-4^41
b) 11*(5^21-5^20-5^18)

Answer 1

a) 2⁸³-4⁴¹=
=2⁸³-2⁸²=
=2⁸²(2¹-2⁰)=
=2⁸²=
=(2⁴¹)²   deci patrat perfect

b) 11*(5²¹-5²⁰-5¹⁸)=
= 11*15¹⁸(5³-5²-5⁰)=
= 11*15¹⁸(125-25-1)=
= 11*15¹⁸ *99=
= 11*15¹⁸ *3² *11=
= 3² *11² *15¹⁸ =
=( 3 *11 *15⁹)²  deci patrat perfect