document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=461590>Question 461590</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a and b are two distinct non-negative numbers, prove that a^4+b^4>ab(a^2+b^2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316524 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=316524\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Not both of a and b are equal to zero, by the given.  Assume one of them, say a, is zero, but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+%3C%3E+0 ALIGN=MIDDLE  ALT=\"b+%3C%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E4+%3E+0%2Ab%2A%280%2Bb%29+=+0 ALIGN=MIDDLE  ALT=\"b%5E4+%3E+0%2Ab%2A%280%2Bb%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is always true.<BR>\n" );
document.write( "Hence assume that both a and b are positive.\r<BR>\n" );
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document.write( "Then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-b%29%5E2%28a%5E2+%2B+ab+%2B+b%5E2%29+%3E+0 ALIGN=MIDDLE  ALT=\"%28a-b%29%5E2%28a%5E2+%2B+ab+%2B+b%5E2%29+%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=%28a-b%29%28a-b%29%28a%5E2+%2B+ab+%2B+b%5E2%29+%3E+0 ALIGN=MIDDLE  ALT=\"%28a-b%29%28a-b%29%28a%5E2+%2B+ab+%2B+b%5E2%29+%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=%28a%5E3-b%5E3%29%28a+-+b%29+%3E+0 ALIGN=MIDDLE  ALT=\"%28a%5E3-b%5E3%29%28a+-+b%29+%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%5E3%28a-b%29+-+b%5E3%28a-b%29+%3E+0 ALIGN=MIDDLE  ALT=\"a%5E3%28a-b%29+-+b%5E3%28a-b%29+%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%5E3%28a-b%29+%2B+b%5E3%28b-a%29+%3E+0+ ALIGN=MIDDLE  ALT=\"a%5E3%28a-b%29+%2B+b%5E3%28b-a%29+%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%5E4+-+a%5E3b+%2B+b%5E4+-+ab%5E3+%3E+0 ALIGN=MIDDLE  ALT=\"a%5E4+-+a%5E3b+%2B+b%5E4+-+ab%5E3+%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%5E4+%2B+b%5E4+%3E+a%5E3b+%2B+ab%5E3 ALIGN=MIDDLE  ALT=\"a%5E4+%2B+b%5E4+%3E+a%5E3b+%2B+ab%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E4+%2B+b%5E4+%3E+ab%28a%5E2+%2B+b%5E2%29 ALIGN=MIDDLE  ALT=\"a%5E4+%2B+b%5E4+%3E+ab%28a%5E2+%2B+b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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