SOLUTION: The sum of two number is 17 and sum of their squares is 145. What are the numbers?

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Question 731033: The sum of two number is 17 and sum of their squares is 145. What are the numbers?
Answer by hoomanc(14) About Me  (Show Source):
You can put this solution on YOUR website!
1) a%2Bb=17 & 2) a%5E2%2Bb%5E2=145
Try to make equation #(2) from equation #(1):
so, a%2Bb=17 >>> %28a%2Bb%29%5E2=17%5E2 >>> %28a%5E2%2Bb%5E2%2B2ab%29=289 >>> from eq. #(2) >>> %28145%2B2ab%29=289 >>> %282ab%29=144 >>> %28ab%29=72
Now use these two new equations: (2) a%2Bb=17 (3) %28ab%29=72
a%2Bb=17 >>> b=17-a substitute in eq. #(3)
%28ab%29=72 >>> %28a%2817-a%29%29=72 >>> a%5E2-17a%2B72=0
%28a-8%29%28a-9%29=0 >>>
(1) a=8 >>> b=9 or the other way,
(2) a=9 >>> b=8