document.write( "Question 178834: Two positive numbers differ by 11, and their square roots differ by 1. Find the numbers \n" ); document.write( "

Algebra.Com's Answer #133822 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
Two positive numbers
\n" ); document.write( "x, y
\n" ); document.write( ":
\n" ); document.write( "differ by 11,
\n" ); document.write( "x-y = 11
\n" ); document.write( "or
\n" ); document.write( "x = (y+11)
\n" ); document.write( ":
\n" ); document.write( " their square roots differ by 1.
\n" ); document.write( " $\"sqrt%28x%29+-+sqrt%28y%29\"$ = 1
\n" ); document.write( ":
\n" ); document.write( " Find the numbers
\n" ); document.write( ":
\n" ); document.write( "Substitute (y+11) for x in the above equation
\n" ); document.write( " $\"sqrt%28y%2B11%29+-+sqrt%28y%29\"$ = 1
\n" ); document.write( ":
\n" ); document.write( " $\"sqrt%28y%2B11%29\"$ = $\"sqrt%28y%29\"$ + 1
\n" ); document.write( ":
\n" ); document.write( "Square both sides
\n" ); document.write( "y + 11 = ( $\"sqrt%28y%29\"$ + 1)^2
\n" ); document.write( ";
\n" ); document.write( "FOIL the right side:
\n" ); document.write( "y + 11 = y + $\"2sqrt%28y%29\"$ + 1
\n" ); document.write( ":
\n" ); document.write( "y - y + 11 - 1 = $\"2sqrt%28y%29\"$
\n" ); document.write( ":
\n" ); document.write( "10 = $\"2sqrt%28y%29\"$
\n" ); document.write( ":
\n" ); document.write( "Square both sides:
\n" ); document.write( "100 = 4y
\n" ); document.write( "y = $\"100%2F4\"$
\n" ); document.write( "y = 25
\n" ); document.write( "then
\n" ); document.write( "x = 25 + 11
\n" ); document.write( "x = 36
\n" ); document.write( ":
\n" ); document.write( "This satisfies the problem as you can see \n" ); document.write( "

\n" );