document.write( "Question 130543: The sum of the squares of two consecutive odd integers is 34. Find the two integers. \n" ); document.write( "

Algebra.Com's Answer #95337 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll do the long (and correct) version of the solution:
\n" ); document.write( "Let the first odd integer be (2x+1) and the next consecutive odd integer be (2x+3)
\n" ); document.write( "Why (2x+1) and (2x+3)?
\n" ); document.write( "This insures that the integers will be odd, no matter what value of integer x you may substitute.
\n" ); document.write( " $\"%282x%2B1%29%5E2%2B%282x%2B3%29%5E2+=+34\"$ \"The sum of the squares of two consecutive odd integers is 35\"
\n" ); document.write( "Simplify and solve for x.
\n" ); document.write( " $\"%282x%2B1%29%5E2%2B%282x%2B3%29%5E2+=+34\"$ Square the terms on the left side.
\n" ); document.write( " $\"%284x%5E2%2B4x%2B1%29%2B%284x%5E2%2B12x%2B9%29+=+34\"$ Simplify.
\n" ); document.write( " $\"8x%5E2%2B16x%2B10+=+34\"$ Subtract 34 from both sides.
\n" ); document.write( " $\"8x%5E2%2B16x-24+=+0\"$ Divide through by 8 to simplify.
\n" ); document.write( " $\"x%5E2%2B2x-3+=+0\"$ Factor this quadratic equation.
\n" ); document.write( " $\"%28x-1%29%28x%2B3%29+=+0\"$ Apply the zero products rule.
\n" ); document.write( " $\"x-1+=+0\"$ or $\"x%2B3+=+0\"$ , so then...
\n" ); document.write( " $\"x+=+1\"$ or $\"x+=+-3\"$
\n" ); document.write( "The integers are:
\n" ); document.write( "For x = 1:
\n" ); document.write( "2x+1 = 2(1)+1 = 3
\n" ); document.write( "2x+3 = 2(1)+3 = 5 and the other pair of integers is:
\n" ); document.write( "For x = -3:
\n" ); document.write( "2x+1 = 2(-3)+1 = -6+1 = -5
\n" ); document.write( "2x+3 = 2(-3)+3 = -3+3 = -3
\n" ); document.write( "So there are two solutions to this problem:
\n" ); document.write( "Consecutive odd integers: 3 and 5
\n" ); document.write( "Consecutive odd integers -5 and -3 \n" ); document.write( "

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