document.write( "Question 657487: I am thinking of two numbers. The sum of the number is 3; the sum of their squares is 29. What are the numbers?
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Algebra.Com's Answer #409925 by KMST(5328) $\"\"$ $\"About$

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Let's call the two numbers $\"x\"$ and $\"y\"$ .
\n" ); document.write( "The problem tells us that $\"x%2By=3\"$ and $\"x%5E2%2By%5E2=29\"$ .
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\n" ); document.write( " $\"x%2By=3\"$ --> $\"%28x%2By%29%5E2=3%5E2\"$ --> $\"x%5E2%2By%5E2%2B2xy=9\"$
\n" ); document.write( "Subtracting $\"x%5E2%2By%5E2=29\"$ from $\"x%5E2%2By%5E2%2B2xy=9\"$ , we get.
\n" ); document.write( " $\"x%5E2%2By%5E2%2B2xy-x%5E2-y%5E2=9-29\"$ --> $\"2xy=-20\"$ --> $\"xy=-10\"$
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\n" ); document.write( "We can find number that satisfy $\"xy=-10\"$ and $\"x%2By=3\"$ .
\n" ); document.write( "We see that $\"highlight%285%29\"$ and $\"highlight%28-2%29\"$ work.
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\n" ); document.write( "We could also set up and solve a quadratic equation
\n" ); document.write( " $\"xy=-10\"$ --> $\"y=-10%2Fx\"$ (dividing both sides by $\"x\"$ )\r
\n" ); document.write( "\n" ); document.write( "and substituting into $\"x%2By=3\"$ , we get
\n" ); document.write( " $\"x-10%2Fx=3\"$ --> $\"x%5E2-10=3x\"$ (multiplying both sides times $\"x\"$ )
\n" ); document.write( "Then $\"x%5E2-10=3x\"$ --> $\"x%5E2-3x-10=0\"$ (subtracting $\"3x\"$ from both sides).
\n" ); document.write( "Of course, we find the same solutions.
\n" ); document.write( "We find $\"x=5\"$ , which leads to $\"y=-2\"$
\n" ); document.write( "and we find $\"x=-2\"$ , which leads to $\"y=5\"$ .
\n" ); document.write( "Either way, the numbers are $\"highlight%285%29\"$ and $\"highlight%28-2%29\"$ .
\n" ); document.write( "It does not matter which number we call $\"x\"$ . \n" ); document.write( "

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