document.write( "Question 975311: If (x-a)(x-b)=1 and a-b+5=0
\n" ); document.write( "Then
\n" ); document.write( "[(x-a)^3-1]/(x-a)^3 = ?\r
\n" ); document.write( "\n" ); document.write( "(X-a) power of 3 -1/(x-a) power of 3=
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #597114 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( " If (x-a)(x-b)=1 and a-b+5=0\r\n" );
document.write( "Then\r\n" );
document.write( "(x-a)^3-1/(x-a)^3 = ?\r\n" );
document.write( "\r\n" );
document.write( "71 +- 13V29\r\n" );
document.write( "\r\n" );
document.write( "Let x-a = u.  Then x = a+u\r\n" );
document.write( "\r\n" );
document.write( "Making those substitutions the problem becomes:\r\n" );
document.write( "\r\n" );
document.write( "If u(a+u-b)=1 and a-b+5=0\r\n" );
document.write( "\r\n" );
document.write( "Then\r\n" );
document.write( "u^3-1/u^3 = ?\r\n" );
document.write( "\r\n" );
document.write( "Since a-b+5=0, then a = b-5\r\n" );
document.write( "\r\n" );
document.write( "Substitute in\r\n" );
document.write( "\r\n" );
document.write( "u(a+u-b)=1\r\n" );
document.write( "\r\n" );
document.write( "u(b-5+u-b) = 1\r\n" );
document.write( "\r\n" );
document.write( "u(-5+u) = 1\r\n" );
document.write( "\r\n" );
document.write( "-5u+u² = 1\r\n" );
document.write( "\r\n" );
document.write( "u²-5u-1 = 0\r\n" );
document.write( "\r\n" );
document.write( "To avoid a conflict of letters, we use capital letters \r\n" );
document.write( "in the quadratic formula\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We want to find : \r\n" );
document.write( "\r\n" );
document.write( "We factor as the difference of two cubes:\r\n" );
document.write( "\r\n" );
document.write( "(1)  \r\n" );
document.write( "\r\n" );
document.write( "We need u², , , and  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let's first use the + sign, \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Rationalizing the denominator:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Going back to equation (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If we do the same with ,\r\n" );
document.write( "all the signs of the terms in  will reverse their signs,\r\n" );
document.write( "and we'll still get 140.\r\n" );
document.write( "\r\n" );
document.write( "Answer: 140\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );