document.write( "Question 65135: Solve for x: sqrt(2x-1) - sqrt(x+3) = 1 \n" ); document.write( "
Algebra.Com's Answer #45623 by funmath(2933)\"\" \"About 
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Solve for x: sqrt(2x-1) - sqrt(x+3) = 1
\n" ); document.write( "\"sqrt%282x-1%29-sqrt%28x%2B3%29%2Bsqrt%28x%2B3%29=sqrt%28x%2B3%29%2B1\"
\n" ); document.write( "\"sqrt%282x-1%29=sqrt%28x%2B3%29%2B1\"
\n" ); document.write( "\"%28sqrt%282x-1%29%29%5E2=%28sqrt%28x%2B3%29%2B1%29%5E2\"
\n" ); document.write( "\"2x-1=sqrt%28%28x%2B3%29%5E2%29%2B2sqrt%28x%2B3%29%2B1\"
\n" ); document.write( "\"2x-1=x%2B3%2B2sqrt%28x%2B3%29%2B1\"
\n" ); document.write( "\"2x-1=x%2B4%2B2sqrt%28x%2B3%29\"
\n" ); document.write( "\"2x-x-1-4=x-x%2B4-4%2B2sqrt%28x%2B3%29\"
\n" ); document.write( "\"x-5=2sqrt%28x%2B3%29\"
\n" ); document.write( "\"%28x-5%29%5E2=%282sqrt%28x%2B3%29%29%5E2\"
\n" ); document.write( "\"x%5E2-10x%2B25=4%28x%2B3%29\"
\n" ); document.write( "\"x%5E2-10x%2B25=4x%2B12\"
\n" ); document.write( "\"x%5E2-10x-4x%2B25-12=4x-4x%2B12-12\"
\n" ); document.write( "\"x%5E2-14x%2B13=0\"
\n" ); document.write( "(x-1)(x-13)=0
\n" ); document.write( "x-1=0 or x-13=0
\n" ); document.write( "x-1+1=0+1 or x-13+13=0+13
\n" ); document.write( "x=1 or x=13 Check for extraneous solutions.
\n" ); document.write( "\"sqrt%282x-1%29-sqrt%28x%2B3%29=1\"
\n" ); document.write( "\"sqrt%282%281%29-1%29-sqrt%281%2B3%29=1\"
\n" ); document.write( "\"sqrt%282-1%29-sqrt%284%29=1\"
\n" ); document.write( "\"sqrt%281%29-sqrt%284%29=1\"
\n" ); document.write( "\"1-2=1\"
\n" ); document.write( "\"-1=1\" False! x=1 is extraneous!
\n" ); document.write( "\"sqrt%282%2813%29-1%29-sqrt%2813%2B3%29=1\"
\n" ); document.write( "\"sqrt%2826-1%29-sqrt%2816%29=1\"
\n" ); document.write( "\"sqrt%2825%29-sqrt%2816%29=1\"
\n" ); document.write( "\"5-4=1\"
\n" ); document.write( "\"1=1\" True! x=13 is a valid solution!!!
\n" ); document.write( "Happy Calculating!!!
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