document.write( "Question 1199421: Prove that if the two larger numbers in a pythagorean triple differ by 1 , then their sum is the square of the smaller number (example 5, 12 ,13 ) \n" ); document.write( "

Algebra.Com's Answer #833293 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Prove that if the two larger numbers in a pythagorean triple differ by 1,
\n" ); document.write( "then their sum is the square of the smaller number (example 5, 12 ,13 )
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document.write( "Let \"a\", \"b\" and \"c\" be a pythagorean triple;\r\n" );
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document.write( "\"b\" abd \"c\" be two larger numbers (with \"c\" be the LARGEST) and \r\n" );
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document.write( "    c - b = 1    (1)   (differ by 1).\r\n" );
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document.write( "Then \r\n" );
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document.write( "    a^2 + b^2 = c^2,\r\n" );
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document.write( "hence,\r\n" );
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document.write( "    a^2 = c^2 - b^2 = (c-b)*(c+b).\r\n" );
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document.write( "Sunstitute here 1 instead of c-b, based on (1), and you will get\r\n" );
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document.write( "    a^2 = b + c.\r\n" );
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document.write( "This equality is what should be proved.\r\n" );
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document.write( "At this point, the proof and the solution of the problem is complete.\r\n" );
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