document.write( "Question 717054: Are there two numbers whose sum is greater then it's product \n" ); document.write( "

Algebra.Com's Answer #440073 by KMST(5328) $\"\"$ $\"About$

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YES.
\n" ); document.write( "That is the short answer. It is a very open-response question. It can be expanded, elaborated, and various statements can be proven.
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\n" ); document.write( "There are pairs of numbers whose sum is greater than their product and there are pairs for whom the product is greater.
\n" ); document.write( "If both numbers are equal or greater than 2, the product will be equal or greater than the sum, so do not look for examples there.
\n" ); document.write( "If we are talking about natural numbers (1, 2, 3, and so on), taking 1 as one of the numbers will always work, but otherwise you would have no solutions.
\n" ); document.write( "So the sets {1,1}, {1,2}, {1,3}, and so on work:
\n" ); document.write( " $\"1%2B1=2%3E1=1%2A1\"$
\n" ); document.write( " $\"1%2B2=3%3E2=1%2A2\"$
\n" ); document.write( " $\"1%2B3=4%3E3=1%2A3\"$
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\n" ); document.write( "If we include zero and negative integers we can have more examples.
\n" ); document.write( "If we extend what we mean by \"numbers\" to rational, or real numbers we can have even more examples.\r
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