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The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?

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m+n=8
m^2+n^2=34

n=8-m
n^2=64-16m+m^2
m^2+n^2=34
m^2+64-16m+m^2=34
2m^2-16m+30=0
m^2-8m+15=0
(m-5)(m-3)=0
the two numbers are 3,5

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