Question

Aflati numerele a si b stiind ca ab+ba cu bara deasupra, respectiv ab- ba cu bara deasupra sunt patrate perfecte

Answer 1

Daca a=n^2 atunci spunem ca a este un patrat perfect.
ab+ba=patrat perfect
ab-ba=patrat perfect
10a+b+10b+a=patrat perfect
11a+11b=patrat perfect
11(a+b)=121
a+b=11
(10a+b)-(10b+a)=patrat perfect
9a-9b=patrat perfect
9(a-b)=9
a-b=1
a+b=11
a-b=1
a=b+1
b+1+b=11
bx2=10
b=10:2
b=5
a=5+1
a=6
proba: 65+56=121(patrat perfect)
           65-56=9(patrat perfect)