Question

Aratati ca numerele: 100 la puterea a 2 - 100 - 99 si 100x102+1 sunt patrate perfecte

Answer 1

100² - 100 - 99
100(100-1) - 99
100 • 99 - 99
9900 - 99
9801 => √9801 = 99

100 • 102 + 1
10200 + 1
10201 => √10201 = 101

Answer 2

100² - 100 - 99 = 100*(100-1) - 99 = 100*99 - 99 = 99(100-1) = 99² = p.p.

100*102+1 = 10200+1=10201=101*101=101² = p.p.