Algebra.Com's Answer #832361 by ikleyn(52784)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "The product of two numbers is 51. Find the numbers if the
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document.write( "sum of three times one number and the other is as large as
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document.write( "possible. Find them if the same sum is as small as possible.
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document.write( "Let one number be x; then the other number is  .\r\n" );
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document.write( "The problem asks two questions:\r\n" );
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document.write( " (a) find real value of x providing the maximum x +  = x +  (if exists);\r\n" );
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document.write( " (b) find real value of x providing the minimum x + = x + (if exists).\r\n" );
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document.write( "Answer to question (a) is THIS:\r\n" );
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document.write( " | such number x does not exist. |\r\n" );
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document.write( " Indeed, we can take positive value of x as large as we want (any real positive number).\r\n" );
document.write( " Then the addend will be small, but still positive, making the sum x + even greater.\r\n" );
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document.write( "Answer to question (b) is SIMILAR:\r\n" );
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document.write( " | such number x does not exist. |\r\n" );
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document.write( " Indeed, we can take negative value of x as small as we want (any real negative number).\r\n" );
document.write( " Then the addend will be negative number, making the sum x + even smaller.\r\n" );
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document.write( "The plot of the function f(x) = x + is shown below.\r\n" );
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document.write( "It makes it graphically obvious my answers, saying that this given function has \r\n" );
document.write( "NEITHER global maximum, NOR global minimum.\r\n" );
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document.write( "  \r\n" );
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document.write( " Plot f(x) =  + \r\n" );
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document.write( "Solved, answered and explained.\r
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document.write( "As worded, the problem has no solution.\r
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document.write( "Function f(x) has local minimum and maximum, but not global minimum and maximum.\r
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document.write( "Therefore, in order for the problem does really have solution/solutions, it should be
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document.write( "worded/posed in different way.\r
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document.write( "How you will pose it in correct way, depends on you - I do not want to guess the ideas
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document.write( "inside your head.\r
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document.write( "The other tutor considers only positive integer numbers in his response,\r
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document.write( "although the problem does not impose these restrictions;\r
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document.write( "so, his answer and his solution/consideration is not relevant to the problem.\r
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