document.write( "Question 271017: The sum of the squares of two consecutive positive odd integers is 130. Find the two integers \n" ); document.write( "

Algebra.Com's Answer #198419 by oberobic(2304) $\"\"$ $\"About$

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x = first positive odd integer
\n" ); document.write( "y = second positive odd integer
\n" ); document.write( "y = x+2 = the second positive odd integer is consecutive to x.
\n" ); document.write( ".
\n" ); document.write( "x +y = 130
\n" ); document.write( "substituting
\n" ); document.write( "x + x+2 = 130
\n" ); document.write( "2x + 2 = 130
\n" ); document.write( "subtracting 2 from both sides
\n" ); document.write( "2x = 128
\n" ); document.write( "dividing both sides by 2
\n" ); document.write( "x = 64, and it is NOT ODD !
\n" ); document.write( "So, there is no solution with odd integers.
\n" ); document.write( ".
\n" ); document.write( "To check, we can explore the relationship of \"nearby\" odd integers:
\n" ); document.write( "x = 65
\n" ); document.write( "y = x+2 = 67
\n" ); document.write( "x+y = 132
\n" ); document.write( ".
\n" ); document.write( "x = 63
\n" ); document.write( "y = x+2 = 65
\n" ); document.write( "x+y = 128
\n" ); document.write( ".
\n" ); document.write( "So there is no solution with consecutive odd numbers.
\n" ); document.write( ".
\n" ); document.write( "If the original problem were to have been x+y = 132, then the solution would have been 65 and 67.
\n" ); document.write( "But that was not what was given. \n" ); document.write( "

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