SOLUTION: two positive numbers differ by 7 and the sum of their squares is 169. find the numbers.

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Question 484760: two positive numbers differ by 7 and the sum of their squares is 169. find the numbers.
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
Let x is the first number
Let y is the second number
two positive numbers differ by 7, so x-y=7
the sum of their squares is 169, so x%5E2%2By%5E2=169
The system of equations
system%28x-y=7%2Cx%5E2%2By%5E2=169%29
From the first equation x=7%2By substitute into the second equation
%287%2By%29%5E2%2By%5E2=169
49%2B14y%2By%5E2%2By%5E2-169=0
2y%5E2%2B14y-120=0divide by 2
y%5E2%2B7y-60=0
y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A1%2A%28-60%29+%29%29%2F%282%2A1%29+
y+=+%28-7+%2B-+sqrt%28289+%29%29%2F2+
y+%5B1%5D=+%28-7+%2B17%29%2F2+=5
y+%5B2%5D=+%28-7+-17%29%2F2+=-12
If y%5B1%5D=5, then x%5B1%5D=7%2B5=12
If y%5B2%5D=-12, then x[2]=7+(-12)=-5}}}
Answer 5 and 12, or -5 and -12