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document.write( "Let a and b be the solutions to 5x^2 - 11x + 4 = -x^2 + 5x - 3.
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document.write( "Find a^2/b + b^2/a
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document.write( "The given equation, after reducing, is equivalent to this quadratic equation\r\n" );
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document.write( " 6x^2 - 16x + 7 = 0. (1)\r\n" );
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document.write( "According to Vieta's theorem, if \"a\" and \"b\" are the roots of this quadratic equation, then\r\n" );
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document.write( " a + b = 
= 
, (2)\r\n" );
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document.write( " ab = 
. (3)\r\n" );
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document.write( "Now, 
+ 
= 
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document.write( "The numerator is\r\n" );
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document.write( " a^3 + b^3 = (a+b)*(a^2 - ab + b^2) = (a+b)*((a^2+2ab+b^2)-3ab) = (a+b)*((a+b)^2-3ab) = (a+b)^3 - 3(a+b)*(ab).\r\n" );
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document.write( "Now replace here (a+b) by 8/3 based on (2) and replace ab by 7/6 based on (3).\r\n" );
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document.write( "You will get \r\n" );
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document.write( " a^3 + b^3 = 
- 
= 
- 
= - 
= 
= 
.\r\n" );
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document.write( "Therefore, 
= 
= 
= 
= 
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document.write( "ANSWER. = .\r\n" );
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document.write( "Solved.\r
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
