SOLUTION: the tens digits of a certain number is 7 less than the units digit .the sum of the squares of the two digits is 85.find the number.with justification

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Question 1146572: the tens digits of a certain number is 7 less than the units digit .the sum of the squares of the two digits is 85.find the number.with justification
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
the tens digits of a certain number is 7 less than the units digit.
                  t = u - 7
the sum of the squares of the two digits is 85.

            t² + u² = 85

Substitute (u - 7) for t:

      (u - 7)² + u² = 85

(u - 7)(u - 7) + u² = 85

 u² - 14u + 49 + u² = 85

     2u² - 14u + 49 = 85

     2u² - 14u - 36 = 0

Divide through by 2

       u² - 7u - 18 = 0 

Factor:

     (u + 2)(u - 9) = 0

 u + 2 = 0;   u - 9 = 0
     u = -2;      u = 9

discard negative answer.

u = 9, substitute in

                 t = u - 7

                 t = 9 - 7

                 t = 2

            NUMBER = 29

Edwin