document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=625084>Question 625084</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If one zero of the function y= x^2 + mx + n is the square of the other, without finding the zeroes, prove that m^3 = n(3m - n - 1).\r<BR>\n" );
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document.write( "Thanks in advance.\r<BR>\n" );
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document.write( "P.S: Is there a method of proving without substitution involved? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #393284 by </B><A HREF=/tutors/aboutme.mpl?userid=oscargut><B>oscargut(2103)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oscargut><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=oscargut><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=393284\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Nice problem !!\r<BR>\n" );
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document.write( "Here is my answer\r<BR>\n" );
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document.write( "y= x^2 + mx + n\r<BR>\n" );
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document.write( "Zeros are: a and a^2\r<BR>\n" );
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document.write( "Sum of the zeros = -m\r<BR>\n" );
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document.write( "a+a^2 = -m\r<BR>\n" );
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document.write( "a(a+1) = -m  (equation 1)\r<BR>\n" );
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document.write( "product of the zeros = n\r<BR>\n" );
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document.write( "a^3 = n   (equation 2)\r<BR>\n" );
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document.write( "From eq 1)and 2)\r<BR>\n" );
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document.write( "(-m)^3 = a^3(a+1)^3 = n(a^3+3a^2+3a+1) = n(n-3m+1)\r<BR>\n" );
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document.write( "Then:  -m^3 = n(n-3m+1)\r<BR>\n" );
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document.write( "m^3 = n(3m-n-1)\r<BR>\n" );
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document.write( "If you have any doubt or if you have  more problems my e-mail is:  \r<BR>\n" );
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document.write( "mthman@gmail.com<BR>\n" );
document.write( " </SPAN>\n" );
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