SOLUTION: The digit of a two-digit number adds up to 14. the number itself is 11 less than the sum of the squares of the digits. find the number Note: I worked out that the two numb

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Question 689851: The digit of a two-digit number adds up to 14. the number itself is 11 less than the sum of the squares of the digits. find the number



Note: I worked out that the two numbers are 5 and 9 by random guessing and substituting the numbers into the question. but I don't know the correct way to set out the working.
Answer by vleith(2983)   (Show Source): You can put this solution on YOUR website!
Let the tens digit be t and the ones digit be 1 .
You are told -->
Also
So



Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 5, 4.5. Here's your graph:

So the only integer answer is o = 5. Which means t = 14-5 = 9
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