document.write( "Question 1181996: Find three consecutive odd integers such that the product of the second and the third integers is twenty-six more than three times the first integer. \n" ); document.write( "

Algebra.Com's Answer #811957 by ikleyn(52778) $\"\"$ $\"About$

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document.write( "Let x be the middle number, so the three consecutive odd numbers are \r\n" );
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document.write( "    (x-2),  x  and  (x+2),   in ascending order.\r\n" );
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document.write( "Then you write the equation as you read the problem\r\n" );
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document.write( "    x*(x+2) = 3*(x-2) + 26.\r\n" );
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document.write( "You simplify this quadratic equation\r\n" );
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document.write( "    x^2 + 2x = 3x - 6 + 26\r\n" );
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document.write( "and write it in the standard form'\r\n" );
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document.write( "    x^2 - x - 20 = 0.\r\n" );
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document.write( "Then you factor its left side\r\n" );
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document.write( "    (x-5)*(x+4) = 0,\r\n" );
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document.write( "and you see that it has the roots  x= 5  and x= -4.\r\n" );
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document.write( "-4 is not an odd number, so the only meaningful solution is  x= 5.\r\n" );
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document.write( "Thus the three numbers are  3,  5,  7.\r\n" );
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document.write( "It is the ANSWER, and you can CHECK it on your own, that the answer satisfies the problem's conditions.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and carefully explained.\r
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