document.write( "Question 353429: The sumof the squares of three consecutive positive integers is 77. Find the integers.
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Algebra.Com's Answer #853706 by ikleyn(53625) $\"\"$ $\"About$

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\n" ); document.write( "The sum of the squares of three consecutive positive integers is 77. Find the integers.
\n" ); document.write( "The book gives a hint: if one integer is x, the next consecutive positive integer is x+1, and the third is x+2
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\n" ); document.write( "\n" ); document.write( " There is much more elegant way to solve, than the way assumed in the book.\r
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document.write( "Let 'n' be the central number of these three consecutive integers.\r\n" );
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document.write( "So, our numbers are (n-1), n and (n+1).\r\n" );
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document.write( "Make an equation for the sum of squares\r\n" );
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document.write( "    (n-1)^1 + n^2 + (n+1)^2 = 77,\r\n" );
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document.write( "    (n^2 - 2n + 1) + n^2 + (n^2 + 2n + 1) = 77,\r\n" );
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document.write( "Cancel opposite terms '-2n' and '2n' and combine like terms\r\n" );
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document.write( "    3n^2 + 2 = 77  --->  3n^2 = 77 - 2  --->  3n^2 = 75  --->  n^2 = 75/3 = 25  --->  n =  = +/- 5.\r\n" );
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document.write( "Since we are looking for positive integer numbers, they are 4, 5 and 6.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, without necessity to solve a quadratic equation.\r
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