SOLUTION: The sum of two numbers is 19, and the sum of their squares is 185. Find the numbers.

Question 796559: The sum of two numbers is 19, and the sum of their squares is 185. Find the numbers.
Found 2 solutions by luke94, Alan3354:
Answer by luke94(89) (Show Source): You can put this solution on YOUR website!
Hi there, not sure of a quicker way to answer but can go through trial and error by testing two numbers that add up to 19 but there squares add to 185
0 + 19 = 0^2 + 19^2 = 361
1 + 18 = 19, 1^2 + 18^2 = 325
2 + 17 = 19, 2^2 + 17^2 = 293
3 + 16 = 19, 3^2 + 16^2 = 265
4 + 15 = 19, 4^2 + 15^2 = 241
5 + 14 = 19, 5^2 + 14^2 = 221
6 + 13 = 19, 6^2 + 13^2 = 205
7 + 12 = 19, 7^2 + 12^2 = 193
8 + 11 = 19, 8^2 + 11^2 = 185

therefore your two numbers are 8 and 11
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The sum of two numbers is 19, and the sum of their squares is 185. Find the numbers.
------------
x + y = 19
x^2 + y^2 = 185
----
y = 19-x
----
x^2 + (19-x)^2 = 185
2x^2 - 38x + 176 = 0
x^2 - 19x + 88 = 0
x = 8, y = 11
x = 11, y = 8
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