SOLUTION: Two positive numbers differ by 5 and the squares of their sum is 169. Find the numbers.

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Question 465944: Two positive numbers differ by 5 and the squares of their sum is 169. Find the numbers.
Answer by sofiyac(983) About Me  (Show Source):
You can put this solution on YOUR website!
x-y=5
%28x%2By%29%5E2=169
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solve this system
x=5+y
%28%285%2By%29%2By%29%5E2=169
25%2B20y%2B4y%5E2=169
4y%5E2%2B20y-144=0 divide everything by 4
y%5E2%2B5y-36=0
(y+9)(y-4)=0
y=-9 y=4 Problem said 2 POSITIVE numbers, so y=-9 won't work.
Which means y=4 is one of the numbers, since we said x-y=5 then x-4=5 so you add 4 to each side and you get x=9
so the numbers are 9 and 4