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

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Question 319442: The sum of two numbers is 8, and the sum of their squares is 34. What is the smaller number?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
a+%2B+b+=+8
a%5E2+%2B+b%5E2+=+34
Using substitution:
a%5E2+%2B+%288+-+a%29%5E2+=+34
a%5E2+%2B+64+-+16a+%2B+a%5E2+=+34
2a%5E2+-+16a+=+-30
a%5E2+-+8a+=+-15
Complete the square:
a%5E2+-+8a+%2B+%288%2F2%29%5E2+=+-15+%2B+%288%2F2%29%5E2
a%5E2+-+8a+%2B+16+=+-15+%2B+16
%28a+-+4%29%5E2+=+1
Take the square root of both sides
a+-+4+=+1
a+=+5
and since
a+%2B+b+=+8
b+=+3
The smaller number is 3
check:
5%5E2+%2B+3%5E2+=+34
25+%2B+9+=+34
34+=+34
OK