document.write( "Question 1062762: Three numbers are in AP such that their sum is 18 and sum of their squares is 158 the greatest number among them is \n" ); document.write( "

Algebra.Com's Answer #677742 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "Three numbers are in AP such that their sum is 18 and sum of their squares is 158 the greatest number among them is
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document.write( "Let x be the middle term of our 3-term AP.\r\n" );
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document.write( "Then  = x-d,  = x and  = x + d, and the sum of the three terms is  (x-d) + x + (x+d) = 3d.\r\n" );
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document.write( "So we have 3x = 18 and x =  = 6.\r\n" );
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document.write( "Next, the square of the first term is  = ,\r\n" );
document.write( "      the square of the middle term is  and\r\n" );
document.write( "      the square of the third term is  = .\r\n" );
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document.write( "Add these tree squares, and you will get their sum as .\r\n" );
document.write( "Now recall that x = 6, hence, x^2 = 36, and the equation for the squares becomes\r\n" );
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document.write( " = 158.\r\n" );
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document.write( "--->   = 158-108 = 50  --->   =  = 25 --->  d = +/- 5.\r\n" );
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document.write( "So, there are two AP progressions satisfying the condition:\r\n" );
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document.write( "1)  6-5 = 1, 6,  6+5 = 11,   and  the reversed sequence\r\n" );
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document.write( "2)  11, 6, 5.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The greatest number of the three is 11.\r
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\n" ); document.write( "\n" ); document.write( "For similar solved problems see the lesson \r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on arithmetic progressions \r
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\n" ); document.write( "\n" ); document.write( "On arithmetic progressions, there is a bunch of lessons\r
\n" ); document.write( "\n" ); document.write( "    - Arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Chocolate bars and arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Mathematical induction and arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - One characteristic property of arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on arithmetic progressions \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
\n" ); document.write( "\"Arithmetic progressions\".\r
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