document.write( "Question 255744: The sum of the squares of two positive consecutive integers is 41. Find integers. Show steps please^^ \n" ); document.write( "

Algebra.Com's Answer #188001 by drk(1908) $\"\"$ $\"About$

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Let x = first integer and x+1 = consecutive integer.
\n" ); document.write( "(i) $\"x%5E2+%2B+%28x%2B1%29%5E2+=+41\"$
\n" ); document.write( "step 1 - expand (i) to get
\n" ); document.write( "(ii) $\"x%5E2+%2B+x%5E2+%2B+2x+%2B+1+=+41\"$
\n" ); document.write( "step 2 - set (i) =0 and factor as
\n" ); document.write( "(iii) $\"2x%5E2+%2B+2x+-40+=+0\"$
\n" ); document.write( "divide by 2 to get
\n" ); document.write( " $\"%28x+-+4+%29%28x+%2B+5%29+=+0\"$
\n" ); document.write( "x-4 = 0 - - -> x = 4
\n" ); document.write( "x+5=0 - - - > x = -5
\n" ); document.write( "SInce we want positive, we have
\n" ); document.write( "x = 4 and x+1 = 5. \n" ); document.write( "

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