document.write( "Question 1101935: the difference between an integer and its square root is 6. find the integer. \n" ); document.write( "

Algebra.Com's Answer #716585 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "This is one example where giving the \"obvious\" answer without showing any work is of little help, because the solution by a formal algebraic process has some things that the student needs to watch our for.

\n" ); document.write( "The given information says $\"x+-+sqrt%28x%29+=+6\"$

\n" ); document.write( "To solve, isolate the radical and square both sides:

\n" ); document.write( " $\"x-6+=+sqrt%28x%29\"$
\n" ); document.write( " $\"x%5E2-12x%2B36+=+x\"$
\n" ); document.write( " $\"x%5E2-13x%2B36+=+0\"$
\n" ); document.write( " $\"%28x-4%29%28x-9%29+=+0\"$

\n" ); document.write( "The possible solutions are x=4 and x=9.

\n" ); document.write( "But since, in solving the equation we squared both sides of the equation, we need to check for extraneous solutions.

\n" ); document.write( "And indeed x=4 does not work: $\"4+-+sqrt%284%29+=+4-2+=+2\"$ is not equal to 6.

\n" ); document.write( "But x=9 works: $\"9+-+sqrt%289%29+=+9-3+=+6\"$ .

\n" ); document.write( "So the single solution is x=9.
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