document.write( "Question 680895: Find two consecutive integers such that the sum of their squares is 85. Find all such integers. \n" ); document.write( "

Algebra.Com's Answer #422504 by JBarnum(2146) $\"\"$ $\"About$

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The 2 consecutive numbers are x and x+1
\n" ); document.write( "So the question in words is the same as below equation:
\n" ); document.write( " $\"%28x%5E2%29%2B%28x%2B1%29%5E2=85\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bx%5E2%2B2x%2B1=85\"$
\n" ); document.write( "Add and simplify
\n" ); document.write( " $\"2x%28x%2B1%29%2B1=85\"$
\n" ); document.write( "Subtract 1 from both sides
\n" ); document.write( " $\"2x%28x%2B1%29=84\"$
\n" ); document.write( "Divide by 2
\n" ); document.write( " $\"x%28x%2B1%29=42\"$
\n" ); document.write( "Distribute
\n" ); document.write( " $\"x%5E2%2Bx=42\"$
\n" ); document.write( "Subtract 42
\n" ); document.write( " $\"x%5E2%2Bx-42=0\"$
\n" ); document.write( "Find 2 numbers that add together that get 1 and multiply to get -42
\n" ); document.write( "They are 7 and -6
\n" ); document.write( " $\"%28x%2B7%29%28x-6%29=0\"$
\n" ); document.write( "X= -7 , 6
\n" ); document.write( "So 2 possible answers
\n" ); document.write( "(-7 and -6) or (6 and 7)
\n" ); document.write( "Check
\n" ); document.write( " $\"6%5E2%2B7%5E2=85\"$
\n" ); document.write( " $\"36%2B49=85\"$
\n" ); document.write( " $\"85=85\"$ \n" ); document.write( "

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