document.write( "Question 1196712: Please l need your help for this assignment.if a and b are the root of the quadratic equation 3x³-4x-7=0, find a²/B +B²/a \n" ); document.write( "
Algebra.Com's Answer #829683 by ikleyn(52797)\"\" \"About 
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\n" ); document.write( "Please l need your help for this assignment.
\n" ); document.write( "If a and b are the root of the quadratic equation 3x³-4x-7=0, find a²/b +b²/a.
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document.write( "From the given part, we have, due to Vieta's formulas\r\n" );
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document.write( "    a + b = \"4%2F3\";  a*b = \"-7%2F3\".     (1)\r\n" );
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document.write( "From the other side,\r\n" );
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document.write( "    \"a%5E2%2Fb\" + \"b%5E2%2Fa\" = \"%28a%5E3+%2B+b%5E3%29%2Fab\".    (2)\r\n" );
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document.write( "The numerator is \r\n" );
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document.write( "    \"a%5E3%2Bb%5E3\" = \"%28a%2Bb%29%2A%28a%5E2+-+ab+%2B+b%5E2%29\" = \"%28a%2Bb%29%2A%28%28a%5E2+%2B+2ab+%2B+b%5E2%29+-+3ab%29%29\" = \r\n" );
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document.write( "            = \"%28a%2Bb%29%2A%28%28a%2Bb%29%5E2-3ab%29\" = now substitute from (1) = \"%284%2F3%29%2A%28%284%2F3%29%5E2+-+3%2A%28-7%2F3%29%29\" = \r\n" );
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document.write( "            = \"%284%2F3%29%2A%28%284%2F3%29%5E2+%2B+7%29%29\" = \"%284%2F3%29%2A%2816%2F9%2B7%29\" = \"%284%2F3%29%2A%28%2816%2B9%2A7%29%2F9%29\" = \"%284%2F3%29%2A%2879%2F9%29\" = \"316%2F27\".\r\n" );
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document.write( "Now we can continue and complete (2) in this way\r\n" );
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document.write( "    \"a%5E2%2Fb\" + \"b%5E2%2Fa\" = \"%28a%5E3+%2B+b%5E3%29%2Fab\" = \"%28%28316%2F27%29%29%2F%28%28-7%2F3%29%29\" = - \"%28316%2A3%29%2F%2827%2A7%29\" = - \"316%2F63\" = -5\"1%2F63\".    ANSWER\r\n" );
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