document.write( "Question 1180669: the difference between a number and it’s positive square root is 12 find the number. \n" ); document.write( "

Algebra.Com's Answer #810408 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "let a number be $\"n\"$ \r
\n" ); document.write( "\n" ); document.write( "if the difference between a number and it’s positive square root is $\"12\"$ , we have\r
\n" ); document.write( "\n" ); document.write( " $\"n-sqrt%28n%29=12\"$
\n" ); document.write( " $\"n-12=sqrt%28n%29\"$ ....square both sides
\n" ); document.write( " $\"%28n-12%29%5E2=%28sqrt%28n%29%29%5E2\"$
\n" ); document.write( " $\"n%5E2-24n%2B144=n\"$
\n" ); document.write( " $\"n%5E2-24n%2B144-n=0\"$
\n" ); document.write( " $\"n%5E2-25n%2B144=0\"$
\n" ); document.write( " $\"n%5E2-25n%2B144=0\"$
\n" ); document.write( " $\"%28n+-+16%29+%28n+-+9%29+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( "solution: \r
\n" ); document.write( "\n" ); document.write( " $\"%28n+-+16%29+=+0\"$ => $\"n=16\"$
\n" ); document.write( " $\"%28n+-+9%29+=+0\"$ => $\"n=9\"$ \r
\n" ); document.write( "\n" ); document.write( "check which solution works\r
\n" ); document.write( "\n" ); document.write( " $\"n-sqrt%28n%29=12\"$ => $\"n=16\"$
\n" ); document.write( " $\"16-sqrt%2816%29=12\"$
\n" ); document.write( " $\"16-4=12\"$
\n" ); document.write( " $\"12=12\"$ -> this solution works\r
\n" ); document.write( "\n" ); document.write( " $\"9-sqrt%289%29=12\"$ => $\"n=9\"$
\n" ); document.write( " $\"9-3=12\"$
\n" ); document.write( " $\"6%3C%3E12\"$ -> this solution does not work\r
\n" ); document.write( "\n" ); document.write( "so, the number is $\"16\"$ \r
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