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 438870: The sum of two numbers is 8, and the sum of their squares is 34. What is the smaller number?
Found 2 solutions by rwm, Gogonati:
Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
x+y=8
x^2+y^2=34
5 and 3

Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Let x the smaller number, then 8-x is the greater. Since their squares is 34, we
get the equation:%288-x%29%5E2%2Bx%5E2=34, we solve this equation:
64-16x%2Bx%5E2%2Bx%5E2-34=0 => 2x%5E2-16x%2B30=0, divide both sides by 2:
x%5E2-8x%2B15=0, solving this equation by factoring we have:
%28x-5%29%28x-3%29=0 x=5 and x=3.
Answer:The smaller number is 3.
Check:3%5E2%2B%288-3%29%5E2=34 => 9%2B25=34 => 34=34.