SOLUTION: the sum of two numbers is 9 and the sum of thier squaresis 41. find the numbers

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Question 216492: the sum of two numbers is 9 and the sum of thier squaresis 41. find the numbers
Answer by Kalmetam(43) About Me  (Show Source):
You can put this solution on YOUR website!
For this problem let number 1 be X and number 2 be Y

X%2BY=9
X%5E2%2BY%5E2=41
There are many ways to solve this... but lets try the most simple way.
Find the Square numbers up to 8
1%5E2=1
2%5E2=4
3%5E2=9
4%5E2=16
5%5E2=25
6%5E2=36
7%5E2=49
8%5E2=64
Right off the bat you can eliminate the last two...
This leaves us with...
1
4
9
16
25
36
The easy way to do it from here is pretend each of those are X... W stands for whole number. Plug in the X's... If 41-X does not equal a whole number, ELIMINATE it.
41-X=W%5E2
Let's try...
41-1=40
40 is not a square number... ELIMINATED a
Next number...
41-4=37
37 is not a square number either... 2 is eliminated
41-9=32
32 is not a square number... and since 3+6=9, 6 is eliminated as well...
This leaves us with 4 and 5 left... let's try..
41-16=25
16=4%5E2
25=5%5E2
The two numbers are 4 and 5.