document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=64609>Question 64609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sqrt(2x-1) - sqrt(x+3) = 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46463 by </B><A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><B>praseenakos@yahoo.com(507)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=praseenakos@yahoo.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=46463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> QUESTION:\r<BR>\n" );
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document.write( "sqrt(2x-1) - sqrt(x+3) = 1\r<BR>\n" );
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document.write( "ANSWER:\r<BR>\n" );
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document.write( "sqrt(2x-1) - sqrt(x+3) = 1\r<BR>\n" );
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document.write( "Squaring on both sides,\r<BR>\n" );
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document.write( "(sqrt(2x-1) - sqrt(x+3))^2 = 1^2\r<BR>\n" );
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document.write( "(2x-1) + (x+3)- 2 sqrt[ (2x-1)(x+3) ] = 1\r<BR>\n" );
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document.write( "2x-1 + x+3 - 2 sqrt[ 2x*x + 2x* 3- 1 * x -1 * 3 ] = 1\r<BR>\n" );
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document.write( "2x + x - 1 + 3 - 2 sqrt[2x^2 + 6x - x - 3 ] = 1\r<BR>\n" );
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document.write( "3x + 2 - 2sqrt [2x^2 + 5x -3] = 1\r<BR>\n" );
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document.write( "3x + 2 - 1 = 2sqrt [2x^2 + 5x -3] \r<BR>\n" );
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document.write( "3x + 1 = 2sqrt [2x^2 + 5x -3] \r<BR>\n" );
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document.write( "Squaring again,\r<BR>\n" );
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document.write( "(3x + 1 )^2 = (2sqrt [2x^2 + 5x -3] )^2\r<BR>\n" );
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document.write( "9x^2 + 6x + 1 = 4  [2x^2 + 5x -3]\r<BR>\n" );
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document.write( "9x^2 + 6x + 1 = 4 * 2x^2 + 4 *5x - 4*3 \r<BR>\n" );
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document.write( "9x^2 + 6x + 1 = 8x^2 + 20x - 12\r<BR>\n" );
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document.write( "9x^2 -8x^2 + 6x  - 20x + 1 + 12 = 0\r<BR>\n" );
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document.write( "1x^2 - 14x + 13 = 0\r<BR>\n" );
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document.write( "x^2 - 14x + 13 = 0\r<BR>\n" );
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document.write( "This is a quadratic equation,\r<BR>\n" );
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document.write( "For solving this equation we have different methods - 1)Using quadratic formula 2) Splitting middle term.\r<BR>\n" );
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document.write( "Splitting middile term:\r<BR>\n" );
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document.write( "x^2 - 14x + 13 = 0\r<BR>\n" );
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document.write( "Here we have to find out two numbers whose sum is -14 and product is +13.<BR>\n" );
document.write( "Such two numbers are -13 and -1\r<BR>\n" );
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document.write( "==> x^2 - 13x - 1x+ 13 = 0\r<BR>\n" );
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document.write( "==> ( x^2 - 13x )- (1x - 13 ) = 0\r<BR>\n" );
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document.write( "==> x (x -13) -1(x-13) = 0\r<BR>\n" );
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document.write( "Take out common terms.\r<BR>\n" );
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document.write( "==> (x-13)(x-1) = 0\r<BR>\n" );
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document.write( "==> either (x-13)= 0  or (x-1) = 0\r<BR>\n" );
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document.write( "==> x = 13   or  x = 1\r<BR>\n" );
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document.write( "So the solution is  x = 13   or  x = 1\r<BR>\n" );
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document.write( "2. Quadratic formula:\r<BR>\n" );
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document.write( "The general form of a quadratic equation is ax^2 + bx + c = 0 and its solution is given by the formula,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ______________________(1)\r<BR>\n" );
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document.write( "Here we have  a = 1, b = -14 and  c = 13\r<BR>\n" );
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document.write( "Substitute these values in (1)\r<BR>\n" );
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document.write( "We have, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28+-14+%29+%2B-+sqrt%28+%28-14%29%5E2-4%2A1%2A13+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28+-14+%29+%2B-+sqrt%28+%28-14%29%5E2-4%2A1%2A13+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814++%2B-+sqrt%28+196+-52%29%29%2F+%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2814++%2B-+sqrt%28+196+-52%29%29%2F+%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814++%2B-+sqrt%28+144%29%29%2F+%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2814++%2B-+sqrt%28+144%29%29%2F+%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814++%2B-+12%29%2F+%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2814++%2B-+12%29%2F+%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "==> x = (14 + 12 )/ 2  or  x = (14 - 12 )/ 2 \r<BR>\n" );
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document.write( "==> x = 26/2 or x = 2/2\r<BR>\n" );
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document.write( "==> x = 13 or x = 1\r<BR>\n" );
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document.write( "In both cases we can see that answers are same.\r<BR>\n" );
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document.write( "Hope you understood.\r<BR>\n" );
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document.write( "Regards.\r<BR>\n" );
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document.write( "Praseena.\r<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( " </SPAN>\n" );
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