document.write( "Question 60809: I have tried this problem a million times and I can not get the answer that the book gives, can someone please show me???
\n" ); document.write( " $\"sqrt%28a%2B7%29=1%2Bsqrt%282a%29\"$
\n" ); document.write( "the book says that the answer is 2 \n" ); document.write( "

Algebra.Com's Answer #41754 by funmath(2933) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%28a%2B7%29=1%2Bsqrt%282a%29\"$
\n" ); document.write( " $\"%28sqrt%28a%2B7%29%29%5E2=%281%2Bsqrt%282a%29%29%5E2\"$
\n" ); document.write( " $\"a%2B7=%281%2Bsqrt%282a%29%29%281%2Bsqrt%282a%29%29\"$
\n" ); document.write( " $\"a%2B7=1%2B2sqrt%282a%29%2B2a\"$
\n" ); document.write( " $\"a-2a%2B7-1=1-1%2B2sqrt%282a%29%2B2a-2a\"$
\n" ); document.write( " $\"-a%2B6=2sqrt%282a%29\"$
\n" ); document.write( " $\"%28-a%2B6%29%5E2=%282sqrt%282a%29%29%5E2\"$
\n" ); document.write( " $\"%28-a%2B6%29%28-a%2B6%29=2%5E2%282a%29\"$
\n" ); document.write( " $\"a%5E2-12a%2B36=4%282a%29\"$
\n" ); document.write( " $\"a%5E2-12a%2B36=8a\"$
\n" ); document.write( " $\"a%5E2-12a-8a%2B36=8a-8a\"$
\n" ); document.write( " $\"a%5E2-20a%2B36=0\"$
\n" ); document.write( "(a-2)(a-18)=0
\n" ); document.write( "a-2=0 and a-18=0
\n" ); document.write( "a=2 and a=18 Check for extraneous solutions:
\n" ); document.write( " $\"sqrt%282%2B7%29=1%2Bsqrt%282%282%29%29\"$
\n" ); document.write( " $\"sqrt%289%29=1%2Bsqrt%284%29\"$
\n" ); document.write( " $\"3=1%2B2\"$
\n" ); document.write( " $\"3=3\"$ a=2 is a valid solution.
\n" ); document.write( " $\"sqrt%2818%2B7%29=1%2Bsqrt%282%2818%29%29\"$
\n" ); document.write( " $\"sqrt%2825%29=1%2Bsqrt%2836%29\"$
\n" ); document.write( " $\"5=1%2B6\"$
\n" ); document.write( " $\"5=7\"$ a=18 is extraneous.
\n" ); document.write( "The only valid solution is a=2.
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "

\n" );