document.write( "Question 53317: two consecutive postive integers sum of squares is 85 \n" ); document.write( "

Algebra.Com's Answer #35579 by EduDragon(8) $\"\"$ $\"About$

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Two consecutive numbers would be $\"n\"$ and $\"%28n%2B1%29\"$ .
\n" ); document.write( "Their squares would be $\"n%5E2\"$ and $\"%28n%2B1%29%5E2\"$ .
\n" ); document.write( "The squares sum would is equal to 85.
\n" ); document.write( "Set the equation so that it looks like this: $\"n%5E2+%2B+%28n%2B1%29%5E2+=+85\"$ .
\n" ); document.write( "Now solve for n.
\n" ); document.write( "First combine all like terms by multiplying out $\"%28n%2B1%29%5E2\"$ . When you do you get $\"n%5E2+%2B+2n+%2B+1\"$ . When you combine all like terms you get $\"2n%5E2+%2B+2n+%2B+1+=+85\"$ .
\n" ); document.write( "Now set the whole equation equal to zero by subtracting 85 from both sides to get: $\"2n%5E2+%2B+2n-84=0\"$ .
\n" ); document.write( "Second, factor out a 2 from everything; that leaves you with $\"2%28n%5E2%2Bn-42%29=0\"$ .
\n" ); document.write( "Factor the parenthesis to get $\"2%28n%2B7%29%28n-6%29=0\"$ .
\n" ); document.write( "Now set each set of parenthesis to zero giving you $\"n%2B7=0\"$ and $\"n-6=0\"$ .
\n" ); document.write( "Solve for n in each case. Do that by either adding or subtracting the appropriate number. This leaves you with $\"n=-7\"$ and $\"n=6\"$ .
\n" ); document.write( "Since the problem wants positive integers you can rule out the -7 leaving the answer to be 6 and, therefore, 7 since you want consecutive integers. \n" ); document.write( "

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