document.write( "Question 998498: three numbers are in arithmetic progression. their sum and sum of their squares is 126. find the smallest number of the arithmetic progression \n" ); document.write( "
Algebra.Com's Answer #616260 by Edwin McCravy(20056)\"\" \"About 
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three numbers are in arithmetic progression. their sum is 18
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document.write( "[The lady above showed that your problem has no solution as\r\n" );
document.write( "you stated it.  That's because you did not give the sum of \r\n" );
document.write( "the numbers and it appeared that the sum of the numbers was \r\n" );
document.write( "also 126.  But since that gives no solution, I arbitrarily \r\n" );
document.write( "assumed it was 18 since that or -18 were the only numbers \r\n" );
document.write( "that would give a reasonable answer.  But please be careful \r\n" );
document.write( "next time to copy the problem exactly.]\r\n" );
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document.write( "Let the three numbers be a-d, a, and a+d.\r\n" );
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document.write( "Those are in arithmetic progression because:\r\n" );
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document.write( "1. If we add d to the first term, which is a-d, we get \r\n" );
document.write( "(a-d)+d or a, which is the second term.\r\n" );
document.write( "2. If we add d to the second term, which is a, we get\r\n" );
document.write( "a+d which is the third term.\r\n" );
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\n" ); document.write( "Their sum is 18 and the sum of their squares is 126.
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document.write( "1)     (a-d)+a+(a+d) = 18\r\n" );
document.write( "2)     (a-d)²+a²+(a+d)² = 126\r\n" );
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document.write( "Simplifying equation 1):\r\n" );
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document.write( "3a = 18\r\n" );
document.write( " a = 6\r\n" );
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document.write( "Substituting a = 6 in the equation 2):\r\n" );
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document.write( "(6-d)²+6²+(6+d)² = 126\r\n" );
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document.write( "Simplifying:\r\n" );
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document.write( "(36-12d+d²)+36+(36+12d+d²) = 126\r\n" );
document.write( "    36-12d+d²+36+36+12d+d² = 126 \r\n" );
document.write( "                   2d²+108 = 126\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "                     d²+54 = 63\r\n" );
document.write( "                        d² = 9\r\n" );
document.write( "                         d = ±3\r\n" );
document.write( "If d = +3, the three terms are, since a = 6\r\n" );
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document.write( "a-d = 6-3 = 3  \r\n" );
document.write( "a = 6 \r\n" );
document.write( "a+d = 6+3 = 9\r\n" );
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document.write( "If d = -3, the three terms are, since a = 6\r\n" );
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document.write( "a-d = 6-(-3) = 6+3 = 9  \r\n" );
document.write( "a = 6 \r\n" );
document.write( "a+d = 6+(-3) = 6-3 = 3\r\n" );
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\n" ); document.write( "find the smallest number of the arithmetic progression
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document.write( "So regardless of whether the the numbers are \r\n" );
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document.write( "3,6,9 or 9,6,3,\r\n" );
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document.write( "The smallest is 3.\r\n" );
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document.write( "Edwin
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