document.write( "Question 59539: what are 2 consecutive positive intergers such that the sum of their squares is 85? \n" ); document.write( "

Algebra.Com's Answer #40803 by Cintchr(481) $\"\"$ $\"About$

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x and x+1 are the integers
\n" ); document.write( " $\"+x%5E2+%2B+%28x%2B1%29%5E2+=+85+\"$
\n" ); document.write( "foil the binomial
\n" ); document.write( " $\"+x%5E2+%2B+x%5E2+%2B+2x+%2B+1+=+85+\"$
\n" ); document.write( "combine like terms
\n" ); document.write( " $\"+2x%5E2+%2B+2x+%2B1+=+85+\"$
\n" ); document.write( "subtract 85 from both sides
\n" ); document.write( " $\"+2x%5E2+%2B+2x+-+84+=+0+\"$
\n" ); document.write( "divide all parts by 2
\n" ); document.write( " $\"+x%5E2+%2B+x+-42+=+0+\"$
\n" ); document.write( "factor
\n" ); document.write( " $\"+%28x%2B7%29%28x-6%29=0+\"$
\n" ); document.write( "set each part equal to zero
\n" ); document.write( " $\"+x%2B7+=+0+\"$ and $\"+x-6=0+\"$
\n" ); document.write( " $\"+x=-7+\"$ and $\"+x=6+\"$
\n" ); document.write( "The stipulation calls for only POSITIVE numbers
\n" ); document.write( " $\"+x=6+\"$
\n" ); document.write( "so ... $\"+x%2B1+=+7+\"$ \r
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\n" ); document.write( "\n" ); document.write( "CHECK
\n" ); document.write( " $\"+6%5E2+%2B+7%5E2+=+85+\"$
\n" ); document.write( " $\"+36+%2B+49+=+85+\"$
\n" ); document.write( " $\"+85+=+85+\"$
\n" ); document.write( "TRUE!!!\r
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