document.write( "Question 1154151: Find three consecutive positive odd integers such that the sum of their squares is 371. \n" ); document.write( "

Algebra.Com's Answer #853826 by greenestamps(13295) $\"\"$ $\"About$

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\n" ); document.write( "For a formal algebraic solution, look at the response from tutor @ikleyn.

\n" ); document.write( "Note that, very often, solving a problem involving an odd number of consecutive integers (or involving an odd number of numbers from ANY arithmetic sequence) is easiest if you let your variable represent the MIDDLE number in the sequence instead of the first. In this problem, observe in her solution that many terms of the resulting polynomials cancel, leaving a much simpler polynomial to work with.

\n" ); document.write( "And if a formal algebraic solution is not required -- as in a competitive math exam where the speed of solving the problem is important -- a quick solution can be found using logical reasoning.

\n" ); document.write( "The sum of the squares of the three consecutive positive odd integers is 371, so the square of the middle one should be approximately 371/3, or about 123. Since 11 squared is 121, it is almost certain that the middle of the integers is 11. Quick mental arithmetic then confirms that 9^2 + 11^2 + 13^2 = 371.

\n" ); document.write( "ANSWER: 9, 11, and 13

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