document.write( "Question 1075905: Given positive integers x and y such that 1/x,+1/y =1/12 , what is the smallest possible value for x + y? \n" ); document.write( "
Algebra.Com's Answer #690557 by math_helper(2461)\"\" \"About 
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The equation \"1%2Fx%2B1%2Fy+=+1%2F12+\" can be re-arranged:
\n" ); document.write( "\"+%28x%2By%29%2Fxy+=+1%2F12+\"
\n" ); document.write( "\"+12%28x%2By%29+=+xy+\" (1)\r
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\n" ); document.write( "\n" ); document.write( "If we think of xy as the area of a rectangle, then the right hand side of (1) is the area, and the left hand side is 6 times the perimeter. The maximum area for minimal perimeter is when the shape is a square (x=y), so let's try x=y:
\n" ); document.write( " \"+12%282x%29+=+x%5E2+\"
\n" ); document.write( " \"++24x+=+x%5E2+\"
\n" ); document.write( " \"+x%5E2+-+24x+=+0+\"
\n" ); document.write( " \"+x%28x-24%29+=+0+\"
\n" ); document.write( " Discard x=0 because x and y are positive integers.
\n" ); document.write( " \"++x=24+\" —> \"+y=24+\"\r
\n" ); document.write( "\n" ); document.write( "So \"+highlight%28x%2By+=+48%29+\" is the minimum value of x+y.
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