### Brain Teasers

# Squares

The square of one whole number minus the square of another whole number equals 73.

What are the two numbers? This can be done by trial and error but a little mathematical knowledge and maybe some algebra will get the answer fast.

What are the two numbers? This can be done by trial and error but a little mathematical knowledge and maybe some algebra will get the answer fast.

### Hint

73 is similar 41,29,19 etc.### Answer

The two numbers are 37 & 36. Therefore (37x37)1369 minus (36x36)1296 = 73. The number 73 is a "prime" number i.e. the only two multiples for it are "73" & "1". By algebra, x2-y2 = 73 which is (x+y)(x-y)=73. One of those two numbers must be "1". It can't be x+y (that would be more than "1") so it must be x-y=1. By simple substitution the answer is revealed.Hide Hint Show Hint Hide Answer Show Answer

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