document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30472>Question 30472</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with the equation:\r<BR>\n" );
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document.write( "sq root of x-9 + sq root of x-21 = sq root of x+11  Solve for x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17118 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sq root of x-9 + sq root of x-21 = sq root of x+11  Solve for x\r<BR>\n" );
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document.write( "sq root of x-9 + sq root of x-21 = sq root of x+11  ----(1)<BR>\n" );
document.write( "Squaring both the sides<BR>\n" );
document.write( "[sqrt of (x-9)]^2 + [sqrt of (x-21)]^2 + 2X[sqrt of (x-9)]X[sqrt of (x-21)] = [sq root of (x+11)]^2<BR>\n" );
document.write( "(x-9)+(x-21)+2X[sqrt of (x-9)]X[sqrt of (x-21)]= (x+11)<BR>\n" );
document.write( "2X[sqrt of (x-9)]X[sqrt of (x-21)]= (x+11)-(x-9)-(x-21)<BR>\n" );
document.write( "=(x-x-x)+(11+9+21)<BR>\n" );
document.write( "=(-x)+(41)<BR>\n" );
document.write( "=(41-x)<BR>\n" );
document.write( "Therefore   2X[sqrt of (x-9)]X[sqrt of (x-21)]= (41-x)<BR>\n" );
document.write( "Squaring both the sides<BR>\n" );
document.write( "{2X[sqrt of (x-9)]X[sqrt of (x-21)]}^2 = [-(x+1)]^2<BR>\n" );
document.write( "4(x-9)(x-21) = (41-x)^2<BR>\n" );
document.write( "4[x(x-21)-9(x-21)] = 1681-82x+x^2<BR>\n" );
document.write( "4(x^2-21x-9x+189)= 1681-82x+x^2<BR>\n" );
document.write( "(4x^2-x^2)+(-84x-36x+82x)+(756-1681)=0  (grouping like terms)<BR>\n" );
document.write( "3x^2-38x-925=0  ----(*)<BR>\n" );
document.write( "Now 3X925= 3X5X185= 3X5X5X37= (3X5X5)X(37)<BR>\n" );
document.write( "The product is (3x^2)X(925)=[-(3X5X5)x]X[(37)x]and -38x= (-75x)+(37x)<BR>\n" );
document.write( "3x^2+[(-75x)+(37x)]-925=0 <BR>\n" );
document.write( "(3x^2-75x)+(37x-925) = 0<BR>\n" );
document.write( "3x(x-25)+37(x-25) = 0<BR>\n" );
document.write( "3xp+37p=0 where p= (x-25)<BR>\n" );
document.write( "p(3x+37) = 0<BR>\n" );
document.write( "That is (x-25)(3x+37)=0<BR>\n" );
document.write( "(x-25)= 0 gives x = 25<BR>\n" );
document.write( "(3x+37)=0 gives x = -37/3<BR>\n" );
document.write( "But x=-37/3 gives <BR>\n" );
document.write( "sq root of x-9 = sq root of(-37/3-9) = sq root of(a negative quantity) which is not defined<BR>\n" );
document.write( "Let us verify for x = 25 in <BR>\n" );
document.write( "sq root of x-9 + sq root of x-21 = sq root of x+11  ----(1)<BR>\n" );
document.write( "LHS = sq root of (25-9) + sq root of (25-21)<BR>\n" );
document.write( "= sq root of 16+ sq root of 4<BR>\n" );
document.write( "= 4 + 2 <BR>\n" );
document.write( "= 6<BR>\n" );
document.write( "= sq root of x+11  for x = 25<BR>\n" );
document.write( "=RHS<BR>\n" );
document.write( "Therefore our value x = 25 is correct<BR>\n" );
document.write( "Answer: x =25\r<BR>\n" );
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document.write( "Remark:The technique used is <BR>\n" );
document.write( "[sqrt(a)+sqrt(b)] = [sqrt(c)]<BR>\n" );
document.write( "squaring<BR>\n" );
document.write( "(a+b)+ 2(sqrta)(sqrtb) =c<BR>\n" );
document.write( "2(sqrta)(sqrtb) = [c-(a+b)]=k say<BR>\n" );
document.write( "2(sqrta)(sqrtb) =k<BR>\n" );
document.write( "squaring<BR>\n" );
document.write( "4ab = k^2 </SPAN>\n" );
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