document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=433306>Question 433306</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove the following inequality. Then state for which values the LHS equals the RHS.\r<BR>\n" );
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document.write( "Please show and explain (in simple terms) every step in the solution.\r<BR>\n" );
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document.write( "a^2 + b^2 >= 2 (a-b-1)\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #300360 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=300360\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I begin with a generally true statement, which is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-1%29%5E2+%2B+%28b%2B1%29%5E2+%3E=+0 ALIGN=MIDDLE  ALT=\"%28a-1%29%5E2+%2B+%28b%2B1%29%5E2+%3E=+0\"   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=a%5E2+-2a+%2B+1+%2B+b%5E2+%2B+2b+%2B+1+%3E=+0 ALIGN=MIDDLE  ALT=\"a%5E2+-2a+%2B+1+%2B+b%5E2+%2B+2b+%2B+1+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+%3E=+2a+-+2b+-+2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+%3E=+2a+-+2b+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+%3E=+2%28a+-+b+-+1%29 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+%3E=+2%28a+-+b+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Equality holds only if a = 1 and b = -1. (This is obvious if you look at the first inequality in this proof.) </SPAN>\n" );
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