document.write( "Question 1190791: Split 69 into three parts such that they are in A. P. and the product of the two smaller parts is 483 \n" ); document.write( "

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document.write( "a1 + a2 + a3 = 69\r
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document.write( "Since we are given a1,a2,a3 form an AP, we can write:\r
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document.write( "a1 + (a1+k) + (a1+2k) = 69    where k is the common difference\r
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document.write( "3a1 + 3k = 69
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document.write( "a1 + k = 23   \r
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document.write( "Trying  a1 = 21,  a1+k = 23, and a1+2k = 25,  we see this AP meets the requiremnt that the first two terms multiply out to 483,  thus  {21,23,25} satisfies the condition.\r
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document.write( "Alternate solution:
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document.write( "a1 * (a1+k) = 483
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document.write( "Expanding it back to a quadratic:
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document.write( "  so we see  a1=21, k=2 works, resulting in {21,23,25} as above\r
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