document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30339>Question 30339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Quesion:<BR>\n" );
document.write( "Solve x^2+y^2=9<BR>\n" );
document.write( "      x+y=3\r<BR>\n" );
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document.write( "(a) (3, -3) (-3, -3)<BR>\n" );
document.write( "(b) (0, -3) (-3, 0)<BR>\n" );
document.write( "(c) (0,0) (3, -3)<BR>\n" );
document.write( "(d) 0, 3) (3, 0) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17007 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=17007\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the given problem is a 1 mark question then you should not try the traditional mathematical analysis given below. You must just try the validity of the choices by the trial and error method.<BR>\n" );
document.write( "You observe that the choice d) holds\r<BR>\n" );
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document.write( "Solve x^2+y^2=9  ----(1)<BR>\n" );
document.write( "      x+y = 3  ----(2)<BR>\n" );
document.write( "Squaring (2)<BR>\n" );
document.write( "(x+y)^2 = 9<BR>\n" );
document.write( "x^2+y^2 +2xy = 9<BR>\n" );
document.write( "(x^2+y^2) +2xy = 9<BR>\n" );
document.write( "9 +2xy =9 (using (1))<BR>\n" );
document.write( "2xy = 9 -9<BR>\n" );
document.write( "2xy = 0<BR>\n" );
document.write( "xy =0/2 = 0<BR>\n" );
document.write( "xy = 0 ----(*) implies atleast one of x or y is 0<BR>\n" );
document.write( "We have by formula<BR>\n" );
document.write( "(x-y)^2 = (x+y)^2-4xy<BR>\n" );
document.write( "(x-y)^2 = 3^2-0 (using (1) and (2) )<BR>\n" );
document.write( "(x-y)^2 =9<BR>\n" );
document.write( "(x-y) = +3 or -3   ----(**)\r<BR>\n" );
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document.write( "Consider x-y = 3 ----(3)<BR>\n" );
document.write( "We have x+y = 3  ----(2)<BR>\n" );
document.write( "(3)+(2) gives (x+x) = (3+3) =6<BR>\n" );
document.write( "2x=6<BR>\n" );
document.write( "x=6/2 = 3<BR>\n" );
document.write( "x= 3 in (3) or in (2) implies y= 0<BR>\n" );
document.write( "Answer: x = 3 and y=0<BR>\n" );
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document.write( "Note: Supposing we consider the other value for (x-y)in (**)<BR>\n" );
document.write( "That is x-y =-3 ----(4)<BR>\n" );
document.write( "We have x+y = 3  ----(2)<BR>\n" );
document.write( "(4)+(2) gives<BR>\n" );
document.write( "2x =0 giving x= 0 and putting x=0 in (2) we get y=3<BR>\n" );
document.write( "So the answer is  x=0 and y= 3<BR>\n" );
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document.write( "Just the role of x and y interchanged.<BR>\n" );
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document.write( "Of the given choices <BR>\n" );
document.write( "the choice  d) holds\r<BR>\n" );
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document.write( "Note: We don't even have to consider the formula<BR>\n" );
document.write( "(x-y)^2 = (x+y)^2-4xy<BR>\n" );
document.write( "as in other problems and then find (x-y) for solving the values of x and y <BR>\n" );
document.write( "because from (*) we have already concluded that one of x or y is ZERO <BR>\n" );
document.write( "and so if we take y= 0 and put it in (2),we get (it orally even) that x=3\r<BR>\n" );
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document.write( " </SPAN>\n" );
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