document.write( "Question 1180203: the sum of the squares of two consecutive numbers is 61.What are those numbers \n" ); document.write( "

Algebra.Com's Answer #853745 by ikleyn(53617) $\"\"$ $\"About$

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\n" ); document.write( "the sum of the squares of two consecutive numbers is 61. What are those numbers
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\n" ); document.write( "\n" ); document.write( "        Two other tutors provided a formal algebra solution.\r
\n" ); document.write( "\n" ); document.write( "        Which is good to develop your technique.\r
\n" ); document.write( "\n" ); document.write( "        But I will give here simple MENTAL solution - - - which is good to develop your mind.\r
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document.write( "The sum of the squares of two consecutive integer numbers is 61.\r\n" );
document.write( "So, we can expect that each of the two squares is about 30 (about half of 61).\r\n" );
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document.write( "Such two squares of integers closest to 30 are 25 and 36 - so check 25 + 36 = 61  <<<---=== correct !\r\n" );
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document.write( "Thus the solution is the pair (5,6).\r\n" );
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document.write( "Recalling the signs, we detect another pair (-6,-5), too.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved MENTALLY.\r
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\n" ); document.write( "\n" ); document.write( "Many other similar problems can be solved similarly.
\n" ); document.write( "It is a good technique to use it in competitions for fastest solution.\r
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