SOLUTION: Two numbers differ by 6. if the numbers are squared and then added, the result is 146. What are the numbers?

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Question 177254: Two numbers differ by 6. if the numbers are squared and then added, the result is 146. What are the numbers?
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
"Two numbers differ by 6" translates to . If we solve for "y", we get

"if the numbers are squared and then added, the result is 146" means that


Start with the second equation.


Plug in


FOIL


Subtract 146 from both sides.


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


Rewrite as


Add to 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 the first numbers are either or


Go back to the isolated equation


Plug in the first solution


Subtract


So when , then

----------------

Go back to the isolated equation


Plug in the first solution


Subtract


So when , then


============================================

Answer:


So this means that the two numbers are

11 and 5

OR

-5 and -11
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