SOLUTION: The sum of squares of two positive integersis is 106. Out of that sum of the greatest number and triple of smallest number is 24, find the numbers.

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Question 1012879: The sum of squares of two positive integersis is 106. Out of that sum of the greatest number and triple of smallest number is 24, find the numbers.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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S=small number; L=large number
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S%5E2%2BL%5E2=106
L%5E2=106-S%5E2
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L%2B3S=24
L=24-3S
L%5E2=%2824-3S%29%5E2=9S%5E2-144S%2B576
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9S%5E2-144S%2B576=106-S%5E2
10S%5E2-144S%2B470=0
5S%5E2-72S%2B235=0
%285S-47%29%28S-5%29=0
5S-47=0 OR S-5=0
5S=47 OR S=5
S=47%2F5 OR S=5
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ANSWER 1: The small number is 5.
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L%2B3S=24
L%2B3%285%29=24
L%2B15=24
L=9
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ANSWER 2: The large number is 9.
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CHECK
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S%5E2%2BL%5E2=106
5%5E2%2B9%5E2=106
25%2B81=106
106=106
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