The difference between two numbers is 3 and the sum of their squares is 117. Find the numbers. Show your full work and the full solution.
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Answer:
6 & 9
Step-by-step explanation:
a and b are the two integers
1. a-b=3
2. a^2+b^2=117
(a-b)^2=3^2 => a^2+b^2-2ab=9 => 117-2ab=9 => 2ab=108 => ab=54
a=b+3--> ab=54 => b(b+3)=54 => b^2+3b-54=0, b=-9(excluded as negative) & b=6
So we get b=6 and a=9
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