document.write( "Question 658159: The difference of two positive numbers is 1 and the sum of their squares is 61. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #410289 by kevwill(135) $\"\"$ $\"About$

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Let the two numbers be x and x+1
\n" ); document.write( " $\"x%5E2+%2B+%28x%2B1%29%5E2+=+61\"$
\n" ); document.write( " $\"x%5E2+%2B+%28x%5E2+%2B+2x+%2B+1%29+=+61\"$
\n" ); document.write( " $\"2x%5E2+%2B+2x+-+60+=+0\"$
\n" ); document.write( " $\"x%5E2+%2B+x+-+30+=+0\"$
\n" ); document.write( "We can solve for x using the quadratic equation $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$ with a=1, b=1, and c=-30:
\n" ); document.write( " $\"x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-30%29+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"x+=+%28-1+%2B-+sqrt%28+1-%28-120%29+%29%29%2F2+\"$
\n" ); document.write( " $\"x+=+%28-1+%2B-+sqrt%28+121+%29%29%2F2+\"$
\n" ); document.write( " $\"x+=+%28-1+%2B-+11%29%2F2+\"$
\n" ); document.write( "And since we're only looking for positive integers:
\n" ); document.write( " $\"x+=+%28-1+%2B+11%29%2F2+\"$
\n" ); document.write( " $\"x+=+10%2F2+=+5+\"$
\n" ); document.write( "So the two numbers are 5 and 6\r
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