SOLUTION: the two-digit number less than 50 is 9 less than the sum of the squares of the digits. What is number?

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Question 291599: the two-digit number less than 50 is 9 less than the sum of the squares of the digits. What is number?
Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
10a+b<50
10a+b=-9+a^2+b^2
a=3,b=6
the number is 36

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
system%2810x%2By%3C50%2C10x%2By=x%5E2%2By%5E2-9%29
The equation is that of a circle:
x%5E2+-10x+%2B+y%5E2+-+y+=+9
Getting it in standard form by completing the square:
x%5E2-10x%2B25%2By%5E2-y%2B1%2F4=9%2B25%2B1%2F4
%28x-5%29%5E2%2B%28y-1%2F2%29%5E2+=+137%2F4
Its center is (5,1%2F2) and its radius is sqrt%28137%29%2F2
The graph is

The only points which appear to have positive integer coefficients
are (3,6) and (7,6). So the number is either 36 or 76. But
since it must be less than 50, the number is 36.
Checking: The sum of the squares of the digits is 3%5E2%2B6%5E2=9%2B36=45
And indeed 45 is 9 more than 36.
Edwin