document.write( "Question 414862: The sum of the reciprocals of two consectutive intergers is 3/2.What are the intergers? \n" ); document.write( "
Algebra.Com's Answer #290965 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
Let the smaller integer be \"x\", then the larger one is \"x+%2B+1\" (since they are consecutive).\r
\n" ); document.write( "\n" ); document.write( "Knowing that the sum of the reciprocals of these two integers is 3 / 2, we obtain an equation:\r
\n" ); document.write( "\n" ); document.write( "\"%281+%2Fx%29+%2B+1%2F%28x+%2B+1%29+=+3+%2F2\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"%28x+%2B+1+%2B+x%29+%2F+%28x%28x+%2B+1%29%29+=+3%2F+2\"...cross multiply\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2%28x+%2B+1+%2B+x%29+=+3x%28x+%2B+1%29\"\r
\n" ); document.write( "\n" ); document.write( "\"2x+%2B+2+%2B+2x+=+3x%5E2+%2B+3x\"\r
\n" ); document.write( "\n" ); document.write( "\"4x+%2B+2++=+3x%5E2+%2B+3x\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"2++=+3x%5E2+%2B+3x-4x\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"+3x%5E2+-x+-2+=0\".........use quadratic formula\r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( " Starting with the general quadratic
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " the general solution using the quadratic equation is:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So lets solve \"3%2Ax%5E2%2Bx-2=0\" ( notice \"a=3\", \"b=1\", and \"c=-2\")
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A3%2A-2+%29%29%2F%282%2A3%29\" Plug in a=3, b=1, and c=-2
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28-1+%2B-+sqrt%28+1-4%2A3%2A-2+%29%29%2F%282%2A3%29\" Square 1 to get 1
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28-1+%2B-+sqrt%28+1%2B24+%29%29%2F%282%2A3%29\" Multiply \"-4%2A-2%2A3\" to get \"24\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28-1+%2B-+sqrt%28+25+%29%29%2F%282%2A3%29\" Combine like terms in the radicand (everything under the square root)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28-1+%2B-+5%29%2F%282%2A3%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28-1+%2B-+5%29%2F6\" Multiply 2 and 3 to get 6
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So now the expression breaks down into two parts
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x+=+%28-1+%2B+5%29%2F6\" or \"x+=+%28-1+-+5%29%2F6\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Lets look at the first part:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=%28-1+%2B+5%29%2F6\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=4%2F6\" Add the terms in the numerator
\n" ); document.write( "
\n" ); document.write( " \"x=2%2F3\" Divide
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So one answer is
\n" ); document.write( "
\n" ); document.write( " \"x=2%2F3\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " Now lets look at the second part:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=%28-1+-+5%29%2F6\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " \"x=-6%2F6\" Subtract the terms in the numerator
\n" ); document.write( "
\n" ); document.write( " \"x=-1\" Divide
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So another answer is
\n" ); document.write( "
\n" ); document.write( " \"x=-1\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( " So our solutions are:
\n" ); document.write( "
\n" ); document.write( " \"x=2%2F3\" or \"x=-1\"
\n" ); document.write( "
\n" ); document.write( "

\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So our solutions are:\r
\n" ); document.write( "\n" ); document.write( "\"x=2%2F3\"....is not an integer, so we discard this solution\r
\n" ); document.write( "\n" ); document.write( " or \"x=-1\"\r
\n" ); document.write( "\n" ); document.write( "If the smaller integer is \"-1\", then the second must be \"-1+%2B+1+=+0\"\r
\n" ); document.write( "\n" ); document.write( "Answer: \"-1\", \"0\"\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );