SOLUTION: I am thinking of two numbers. The sum of the number is 3; the sum of their squares is 29. What are the numbers?

Question 657487: I am thinking of two numbers. The sum of the number is 3; the sum of their squares is 29. What are the numbers?

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Let's call the two numbers and .
The problem tells us that and .

--> -->
Subtracting from , we get.
--> -->

We can find number that satisfy and .
We see that and work.

We could also set up and solve a quadratic equation
--> (dividing both sides by )
and substituting into , we get
--> (multiplying both sides times )
Then --> (subtracting from both sides).
Of course, we find the same solutions.
We find , which leads to
and we find , which leads to .
Either way, the numbers are and .
It does not matter which number we call .
RELATED QUESTIONS
Im thinking of a number. The difference of the two numbers is 36. Their sum is 286. What... (answered by ikleyn)

i am thinking of two consecutive odd numbers. their sum is 112. what are the two... (answered by ewatrrr)

I am thinking of two consecutive odd integers. The sum of their squares is 130. Find... (answered by Alan3354)

I am thinking of two numbers. Their sum is 17' and one number is 5 more than the other.... (answered by rfer)

two numbers differ by 7 and the sum of their squares is 29. find the numbers (answered by JBarnum,Stitch)

I am thinking of two consecutive even integers. The sum of their squares is 340. What are (answered by jorel1380)

Jack is thinking of two positive numbers, one of them is 4 more than the other and the... (answered by algebrahouse.com)

The sum of two numbers is 29. Their difference is 7. What are the two... (answered by uma)

The sum of two numbers is 29. Their difference is 7. What are the two... (answered by checkley71)