document.write( "Question 626301: find 3 consecutive positive odd integers such that the sum of the squares of the first and second integers is equal to the square of the third integer plus 33 \n" ); document.write( "

Algebra.Com's Answer #394105 by Edwin McCravy(20055) $\"\"$ $\"About$

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find 3 consecutive positive odd integers such that the sum of the squares of the first and second integers is equal to the square of the third integer plus 33
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document.write( "Smallest odd integer = x-2\r\n" );
document.write( "Middle-sized odd integer = x\r\n" );
document.write( "Largest odd integer = x+2\r\n" );
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document.write( "               (x-2)² + x² = (x+2)² + 33\r\n" );
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document.write( "      (x-2)² - (x+2)² = 33 - x²\r\n" );
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document.write( "[(x-2)-(x+2)][(x-2)+(x+2)] = 33-x²\r\n" );
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document.write( "        [x-2-x-2][x-2+x+2] = 33-x²\r\n" );
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document.write( "                  [-4][2x] = 33-x²\r\n" );
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document.write( "                       -8x = 33-x²\r\n" );
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document.write( "                  x²-8x-33 = 0\r\n" );
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document.write( "               (x-11)(x+3) = 0\r\n" );
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document.write( "                  x-11 = 0    x+3 = 0\r\n" );
document.write( "                     x = 11     x = -3\r\n" );
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document.write( "We only want the positive odd integers so we \r\n" );
document.write( "ignore the negative answer.\r\n" );
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document.write( "Smallest odd integer = x-2 = 11-2 = 9\r\n" );
document.write( "Middle-sized odd integer = x = 11\r\n" );
document.write( "Largest odd integer = x+2 = 11+2 = 13\r\n" );
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document.write( "Edwin

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