document.write( "Question 342226: How do you solve √(4y+5)-√(y-1)=3 \n" ); document.write( "

Algebra.Com's Answer #245002 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%284y%2B5%29-sqrt%28y-1%29=3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"sqrt%284y%2B5%29=sqrt%28y-1%29%2B3\"$
\n" ); document.write( "Square both sides,
\n" ); document.write( " $\"4y%2B5=%28y-1%29%2B6sqrt%28y-1%29%2B9\"$
\n" ); document.write( " $\"4y%2B5=y%2B8%2B6sqrt%28y-1%29\"$
\n" ); document.write( " $\"3y-3=6sqrt%28y-1%29\"$
\n" ); document.write( " $\"3%28y-1%29=6sqrt%28y-1%29\"$
\n" ); document.write( " $\"%28y-1%29=2sqrt%28y-1%29\"$
\n" ); document.write( "Use a substitution, let $\"u=y-1\"$
\n" ); document.write( " $\"u=2%2Asqrt%28u%29\"$
\n" ); document.write( "Square both sides,
\n" ); document.write( " $\"u%5E2=4u\"$
\n" ); document.write( " $\"u%5E2-4u=0\"$
\n" ); document.write( " $\"u%28u-4%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"u=0\"$
\n" ); document.write( " $\"y-1=0\"$
\n" ); document.write( " $\"highlight%28y=1%29\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"u-4=0\"$
\n" ); document.write( " $\"y-1-4=0\"$
\n" ); document.write( " $\"y-5=0\"$
\n" ); document.write( " $\"highlight%28y=5%29\"$ \n" ); document.write( "

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