Question

aflati cifrele a si b stiind ca ab+ba,respectiv ab-ba sunt patrate perfecte

Answer 1

ab+ba=patrat perfect
ab-ba=patrat perfect
=10a+b+10b+a=
=11a+11b=
=11(a+b)=121=11^2
a+b=121:11
a+b=11
ab-ba=
=(10a+b)-(10b+a)=
=9a-9b=
=9(a-b)=9=3^2
 a-b=9:9
 a-b=1
a+b=11
a-b=1
 a=b+1
b+1+b=11
bx2+1=11
bx2=11-1
bx2=10
b=10:2
b=5
a=5+1
a=6
proba:65+56=121=11^2(patrat perfect)
          65-56=9=3^2(patrat perfect)