SOLUTION: Hi, Can you help me with this math problem? Solve the problem. 15.) The sum of the squares of the digits of a positive two-digit number is 20, and the tens digit is 2 mor

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Question 136740: Hi,
Can you help me with this math problem?
Solve the problem.
15.) The sum of the squares of the digits of a positive two-digit number is 20, and the tens digit is 2 more than the units digit. Find the number.
The answer should be 42
Found 2 solutions by solver91311, Earlsdon:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!
If x is the 10s digit and y is the 1s digit, we know that and

First, substitute for in :

Now, expand the binomial, collect like terms, move the constant term to the left side setting the entire expression equal to zero. That gives you a quadratic that you can solve by factoring. Exclude the negative root because it is extraneous introduced by the act of squaring the variable. The other root will be the value of the 1s digit and you can easily calculate the 10s digit given that information.

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Try this!
Let T = the ten's digit and U = the unit's digit.
Then:
and...
Substitute this into the above equation:
Simplify:

Subtract 20 from both sides.
Factor out a 2.
Apply the zero products rule.
Factor.
so...
or , then...
or Discard the negative solution.
This is the unit's digit.

This is the ten's digit.
The number (TU) is 42.