document.write( "Question 228697: Find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 7 times the third. \n" ); document.write( "

Algebra.Com's Answer #169706 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
Three positive consecutive integers: x, (x+1), (x+2)
\n" ); document.write( ":
\n" ); document.write( "Find three consecutive positive integers such that the product of the first
\n" ); document.write( " and third, minus the second, is 1 more than 7 times the third.
\n" ); document.write( ":
\n" ); document.write( "x(x+2) - (x+1) = 7(x+2) + 1
\n" ); document.write( ":
\n" ); document.write( "x^2 + 2x - x - 1 = 7x + 14 + 1
\n" ); document.write( ":
\n" ); document.write( "x^2 + x - 1 = 7x + 15
\n" ); document.write( ":
\n" ); document.write( "Combine like terms on the left:
\n" ); document.write( "x^2 + x - 7x - 1 - 15 = 0
\n" ); document.write( ":
\n" ); document.write( "x^2 - 6x - 16 = 0; our old friend, the quadratic equation!
\n" ); document.write( "Factors to
\n" ); document.write( "(x - 8)(x + 2) = 0
\n" ); document.write( "We only want the positive solution in this problem
\n" ); document.write( "x = 8, is the 1st integer, then 9, 10; obviously.
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Check our solution in the statement:
\n" ); document.write( "\"the product of the first and third, minus the second, is 1 more than 7 times the third.
\n" ); document.write( "\"
\n" ); document.write( "8*10 - 9 = 7*10 + 1
\n" ); document.write( "80 - 9 = 70 + 1; confirms our solution \n" ); document.write( "

\n" );