document.write( "Question 1166202: The product of two consecutive odd integers is 63.Find the numbers.\r
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Algebra.Com's Answer #790693 by ikleyn(52851) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "1)  First, you may simply GUESS the answer:  63 = 7*9.\r\n" );
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document.write( "    When you guessed it, your next thought is that two opposite numbers give the same product\r\n" );
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document.write( "    and also represent two consecutive odd integers -9,-7.\r\n" );
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document.write( "    So, by guessing, you have these two answers (two pairs)  (7,9)  and  (-9,-7).\r\n" );
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document.write( "2)  You may also take the square root of 63:    is somewhere close to   = 8.\r\n" );
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document.write( "    Therefore, your next thought is about the numbers 7 and 9,\r\n" );
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document.write( "    and then you continue as in n.1).\r\n" );
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document.write( "3)  You may denote the smaller of the two consecutive odd numbers as x;  then the next odd integer number is (x+2).\r\n" );
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document.write( "    In this way, you get this equation\r\n" );
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document.write( "       x*(x+2) = 63.\r\n" );
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document.write( "    You reduce it then to the standard algebraic form\r\n" );
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document.write( "       x^2 + 2x - 63 = 0.\r\n" );
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document.write( "    You may solve it by factoring \r\n" );
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document.write( "       (x+9)*(x-7) = 0\r\n" );
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document.write( "    which gives you the roots  x= -9,  x= 7.\r\n" );
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document.write( "    The first root gives the solution (the pair) (-9,-7);  the other root gives you the pair (7,9).\r\n" );
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document.write( "    We just observed these pairs in the above version 1) and 2).\r\n" );
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document.write( "    You also may solve equation (1) using the quadratic formula.\r\n" );
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\n" ); document.write( "\n" ); document.write( "So, I presented you ALL POSSIBLE WAYS to solve the problem.\r
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