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 #616252 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "Let x be a middle term of this arithmetic progression.\r
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\n" ); document.write( "\n" ); document.write( "Then two other terms are x-d and x+d, where d is the common difference.\r
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\n" ); document.write( "\n" ); document.write( "The sum of three members is   (x-d) + x + (x+d) = 3x.\r
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\n" ); document.write( "\n" ); document.write( "It is 126, hence,   x = $\"126%2F3\"$ = 42.\r
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\n" ); document.write( "\n" ); document.write( "Now, we need to find d. For it, we have another equation\r
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\n" ); document.write( "\n" ); document.write( " $\"%2842-d%29%5E2+%2B+42%5E2+%2B+%2842%2Bd%29%5E2\"$ = $\"126\"$ ,     or\r
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\n" ); document.write( "\n" ); document.write( " $\"42%5E2+-2%2A42%2Ad+%2B+d%5E2+%2B+42%5E2+%2B+42%5E2%5E2+%2B+2%2A42%2Ad+%2B+d%5E2\"$ = $\"126\"$ ,     or\r
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\n" ); document.write( "\n" ); document.write( " $\"2d%5E2+%2B+3%2A42%5E2\"$ = $\"126\"$ ,\r
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\n" ); document.write( "\n" ); document.write( " $\"2d%5E2\"$ = $\"126+-+3%2A42%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Hey, the right side is negative! While the left side is always non-negative. \r
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\n" ); document.write( "\n" ); document.write( "Your problem has no solution. \r
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\n" ); document.write( "\n" ); document.write( "Truly, I spent my time for nothing, working on this problem.\r
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