SOLUTION: The sum of two numbers is 8. The sum of the squares of the two numbers is 34. Find the numbers. I know they are 3 and 5, but how do I show I arrived at that answer

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Question 144981: The sum of two numbers is 8. The sum of the squares of the two numbers is 34. Find the numbers.
I know they are 3 and 5, but how do I show I arrived at that answer
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
"The sum of two numbers is 8" translates to


"The sum of the squares of the two numbers is 34" translates to


Start with the first equation


Subtract x from both sides to isolate y


Move onto the second equation


Plug in


Foil


Get all terms to the left side.


Combine like terms.


Notice we have a quadratic equation in the form of where , , and


Let's use the quadratic formula to solve for x


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Subtract from to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So our answers are or
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