document.write( "Question 997811: The sum of three numbers in a.p is 12 and the sum of their squares is 66. what are the numbers \n" ); document.write( "

Algebra.Com's Answer #615774 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Let x be a middle number, then the first one is x-d and the third one is x+d, where d is the common difference.\r
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\n" ); document.write( "\n" ); document.write( "The sum of three is 12. It means that \r
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\n" ); document.write( "\n" ); document.write( "(x-d) + x + (x+d) = 12,     or \r
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\n" ); document.write( "\n" ); document.write( "3x = 12,     x = $\"12%2F3\"$ = 4. \r
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\n" ); document.write( "\n" ); document.write( "The sum of squares is 66. It means that\r
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\n" ); document.write( "\n" ); document.write( " $\"%284-d%29%5E2+%2B+4%5E2+%2B+%284%2Bd%29%5E2\"$ = $\"66\"$ ,     or\r
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\n" ); document.write( "\n" ); document.write( " $\"16+-+8d+%2B+d%5E2\"$ + $\"16\"$ + $\"16+%2B+8d+%2B+d%5E2\"$ = $\"66\"$ ,\r
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\n" ); document.write( "\n" ); document.write( " $\"48\"$ + $\"2d%5E2\"$ = $\"66\"$ ,\r
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\n" ); document.write( "\n" ); document.write( " $\"2d%5E2\"$ = $\"66-48\"$ ,\r
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\n" ); document.write( "\n" ); document.write( " $\"2d%5E2\"$ = $\"18\"$ , \r
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\n" ); document.write( "\n" ); document.write( " $\"d%5E2\"$ = $\"18%2F2\"$ = $\"9\"$ ,   d = +/- $\"3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Thus our progression is   1, 4, 7   or   7, 4, 1.\r
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