document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=67977>Question 67977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please please helpme this:\r<BR>\n" );
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document.write( "1. Let a,b,c be the three distinct positive real numbers.<BR>\n" );
document.write( "Thank you very for your great help!!!!!!!<BR>\n" );
document.write( "a) Prove that a^3+b^3>a^2xb+b^2xa.<BR>\n" );
document.write( "b) Write down , without proving them, similar inequalities for (a^3+c^3) and (b^3+c^3).<BR>\n" );
document.write( "c) Hence, or otherwise, prove that 3(a^3+b^3+c^3)>(a^2+b^2+c^2)(a+b+c)\r<BR>\n" );
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document.write( "2.State why (a-b)^2(a^2+b^2) is non-negative, for all a,b belong to R. Deduce that a^4+b^4is greater or equal to 2(a^3xb-a^2xb^2+axb^3).\r<BR>\n" );
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document.write( "Thanks a million!!! I am waiting for a solution for ages. Please help me , i am desperate...<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48344 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=48344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Could someone please please helpme this:<BR>\n" );
document.write( "1. Let a,b,c be the three distinct positive real numbers.<BR>\n" );
document.write( "Thank you very for your great help!!!!!!!<BR>\n" );
document.write( "a) Prove that a^3+b^3>a^2xb+b^2xa.................1\r<BR>\n" );
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document.write( "TST<BR>\n" );
document.write( "A^3+B^3-A^2B-B^2A>0<BR>\n" );
document.write( "TST<BR>\n" );
document.write( "A^2(A-B)-B^2(A-B)>0 <BR>\n" );
document.write( "TST<BR>\n" );
document.write( "(A^2-B^2)(A-B)>0<BR>\n" );
document.write( "TST<BR>\n" );
document.write( "(A+B)(A-B)(A-B)>0<BR>\n" );
document.write( "TST<BR>\n" );
document.write( "(A+B)(A-B)^2>0<BR>\n" );
document.write( "IN LHS  (A-B)^2 IS ALWAYS POSITIVE AS IT IS A PERFECT SQUARE AND A AND B ARE DISTINCT<BR>\n" );
document.write( "A+B IS ALSO POSITIVE AS A AND B ARE POSITIVE <BR>\n" );
document.write( "HENCE THEIR PRODUCT IS ALWAYS +VE...PROVED\r<BR>\n" );
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document.write( "b) Write down , without proving them, similar inequalities for (a^3+c^3) and (b^3+c^3).<BR>\n" );
document.write( "A^3+C^3>A^2C+C^2A.................2<BR>\n" );
document.write( "B^3+C^3>B^2C+C^2B................3<BR>\n" );
document.write( "ADDING 1,2,3<BR>\n" );
document.write( "2(A^3+B^3+C^3)>\r<BR>\n" );
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document.write( "c) Hence, or otherwise, prove that 3(a^3+b^3+c^3)>(a^2+b^2+c^2)(a+b+c)<BR>\n" );
document.write( "ADDING 1,2,3<BR>\n" );
document.write( "2(A^3+B^3+C^3)>A^2B+B^2A+B^2C+C^2B+C^2A+A^2C<BR>\n" );
document.write( "ADDING A^3+B^3+C^3 TO BOTH SIDES<BR>\n" );
document.write( "3(A^3+B^3+C^3)>A^3+B^3+C^3+A^2B+B^2A+B^2C+C^2B+C^2A+A^2C=(A^2+B^2+C^2)(A+B+C)<BR>\n" );
document.write( "THE LAST ONE IS A STANDARD FORMULA..IF YOU WANT ITS PROOF PLEASE COME BACK..YOU CAN MULTIPLY AND CHECK FOR YOUR SELF.\r<BR>\n" );
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document.write( "2.State why (a-b)^2(a^2+b^2) is non-negative, for all a,b belong to R.<BR>\n" );
document.write( "(A-B)^2 BEING A PERFECT SQUARE>=0<BR>\n" );
document.write( "A^2+B^2=SUM OF PERFECT SQUARES WHICH IS >=0<BR>\n" );
document.write( "HENCE THEIR PRODUCT IS>=0\r<BR>\n" );
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document.write( " Deduce that a^4+b^4is greater or equal to 2(a^3xb-a^2xb^2+axb^3).<BR>\n" );
document.write( "(A-B)^2(A^2+B^2)=(A^2+B^2-2AB)(A^2+B^2)<BR>\n" );
document.write( "=A^4+A^2B^2+B^2A^2+B^4-2A^3B-2AB^3>=0.........AS PROVED<BR>\n" );
document.write( "A^4+B^4>=2(A^3B-A^2B^2+B^3A).....PROVED\r<BR>\n" );
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document.write( "Thanks a million!!! I am waiting for a solution for ages. Please help me , i am desperate... </SPAN>\n" );
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