SOLUTION: The sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. The square of either of the digits of either number, minus the product o

Question 99998: The sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. The square of either of the digits of either number, minus the product of both digits, plus the square of the other digit is the number 21. What are the numbers?
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
Define the digit as: 10a + b or as a,b where a and b are interchangeable
a + b = 9 or b = 9 - a
and
a^2 - ab + b^2 = 21
a^2 - a(9 - a) + (9 - a)^2 = 21
a^2 - 9a + a^2 + 81 - 18a + a^2 = 21
3a^2 - 27a + 60 = 0
3a^2 - 12a - 15a + 60 = 0
(3a^2 - 12a) + (-15a + 60) = 0
3a(a - 4) - 15(a - 4) = 0
(3a - 15)(a - 4) = 0
a = 4 or a = 15/3
a = 4 ... b = 9 - a = 9 - 4 = 5
45 ... or 54 because a and b are interchangeable
a = 15/3 = 5 ...
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