document.write( "Question 364929: Find solution to :\r
\n" ); document.write( "\n" ); document.write( "[sqrt](2k-1) - [sqrt](k-1) = 1 \r
\n" ); document.write( "\n" ); document.write( "So far I have added [sqrt](k-1) to both sides of equation in order to isolate one radical.\r
\n" ); document.write( "\n" ); document.write( "Now I have to square both sides
\n" ); document.write( "([sqrt](2k-1))squared = ([sqrt](k-1) +1)squared\r
\n" ); document.write( "\n" ); document.write( "2k-1= ([sqrt](k-1)+1))*([sqrt](k-1)+1))\r
\n" ); document.write( "\n" ); document.write( "Somewhere later in my problem I think I am not simplifying correctly. I ended up with :
\n" ); document.write( "(k-1)/2 = [sqrt]k-1\r
\n" ); document.write( "\n" ); document.write( "so then I was back to squaring both sides of my equation\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #260153 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%282k-1%29+-+sqrt%28k-1%29+=+1\"$
\n" ); document.write( "Transpose to get $\"sqrt%282k-1%29+=+sqrt%28k-1%29+%2B+1\"$ .
\n" ); document.write( "Square both sides: $\"2k-1+=+1%2B2sqrt%28k-1%29+%2B+k-1\"$ .
\n" ); document.write( "Simplify: $\"k-1+=+2sqrt%28k-1%29\"$ .
\n" ); document.write( "Square both sides again: $\"k%5E2-2k%2B1+=+4%28k-1%29\"$ ,
\n" ); document.write( " $\"k%5E2-2k%2B1+=+4k-4%29\"$ ,
\n" ); document.write( "or $\"k%5E2+-+6k%2B5+=+0\"$ ,
\n" ); document.write( "then (k-5)(k-1) = 0, or k = 5 or k = 1.
\n" ); document.write( "Both satisfy the original equation, so the solution set is {1,5}.
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