document.write( "Question 1202304: The sum of the squares of two numbers is 218 and their difference multiplied by the smaller number equals 42. Find the two numbers. \n" ); document.write( "
Algebra.Com's Answer #837032 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The solution above is incomplete for there are two solutions.\r\n" );
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document.write( "Let the smaller number be x and the larger number be x+k where k > 0\r\n" );
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document.write( "\"system%28x%5E2%2B%28x%2Bk%29%5E2=218%2C%28k%2Bx-x%29x=42%29\"\r\n" );
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document.write( "\"system%28x%5E2%2Bx%5E2%2B2kx%2Bk%5E2=218%2Ckx=42%29\"\r\n" );
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document.write( "\"system%282x%5E2%2B2kx%2Bk%5E2=218%2Ckx=42%29\"\r\n" );
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document.write( "\"x=42%2Fk\"\r\n" );
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document.write( "\"2%2842%2Fk%29%5E2%2B2k%2842%2Fk%29%2Bk%5E2=218\"\r\n" );
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document.write( "\"2%281764%5E%22%22%2Fk%5E2%29%2B84%2Bk%5E2=218\"\r\n" );
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document.write( "\"3528%5E%22%22%2Fk%5E2%2Bk%5E2=134\"\r\n" );
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document.write( "\"3528%2Bk%5E4=134k%5E2\"\r\n" );
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document.write( "\"k%5E4-134k%5E2%2B3528=0\"\r\n" );
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document.write( "Believe it or not, that factors!:\r\n" );
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document.write( "\"%28k%5E2-36%29%28k%5E2-98%29=0\"\r\n" );
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document.write( "  <--[Remember that k > 0]\r\n" );
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document.write( "Using k = 6, substituting in\r\n" );
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document.write( "\"x=42%2Fk\"\r\n" );
document.write( "\"x=42%2F6=7\"\r\n" );
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document.write( "smaller = 7, larger = 7+6 = 13   <--one answer\r\n" );
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document.write( "Using \"k=7sqrt%282%29\"\r\n" );
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document.write( "\"x=42%2Fk\"\r\n" );
document.write( "\"x=42%2F%287sqrt%282%29%29\"\r\n" );
document.write( "\"x=6%2Fsqrt%282%29\"\r\n" );
document.write( "\"x=%286%2Fsqrt%282%29%29%28sqrt%282%29%2Fsqrt%282%29%29\"\r\n" );
document.write( "\"x=6sqrt%282%29%2F2\"\r\n" );
document.write( "\"x=3sqrt%282%29\"\r\n" );
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document.write( "\"smaller=3sqrt%282%29\"    \"larger=3sqrt%282%29%2B7sqrt%282%29=10sqrt%282%29\"  <--second answer\r\n" );
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document.write( "Edwin
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