document.write( "Question 735490: I have an algebra project and one of the questions says \" The difference between two perfect squares is 133.What is the smallest possible sum of the two perfect squares? \" I found out that the answer is 205, but I don't understand why that is the answer. \n" ); document.write( "
Algebra.Com's Answer #449438 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "       x² - y² = 133\r\n" );
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document.write( "(x - y)(x + y) = 133\r\n" );
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document.write( "So (x - y) and (x + y) are factors of 133\r\n" );
document.write( "and (x - y) is the smaller factor and (x + y) \r\n" );
document.write( "is the larger factor. \r\n" );
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document.write( "The only two ways to factor 133 are\r\n" );
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document.write( "1·133 where 1 is the smaller and 133 is the larger.  \r\n" );
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document.write( "and\r\n" );
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document.write( "7·19  where 7 is the smaller and 19 is the larger.\r\n" );
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document.write( "In the first case we have\r\n" );
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document.write( "x - y = 1\r\n" );
document.write( "x + y = 133\r\n" );
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document.write( "Solve that system and get solution x=67, y=66\r\n" );
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document.write( "The sum of their squares is 67²+66² = 4489 + 4356 = 8845 \r\n" );
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document.write( "In the second case we have\r\n" );
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document.write( "x - y = 7\r\n" );
document.write( "x + y = 19\r\n" );
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document.write( "Solve that system and get solution  x=13, y=6\r\n" );
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document.write( "The sum of their squares is 13²+6² = 169 + 36 =  205\r\n" );
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document.write( "Edwin
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