document.write( "Question 1087154: a,b,c are roots of 2x^3+x^2-7, find value of (a/b+b/a)+(b/c+c/b)+(c/a+a/c) \n" ); document.write( "
Algebra.Com's Answer #701447 by ikleyn(52788)\"\" \"About 
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\n" ); document.write( "a,b,c are roots of 2x^3+x^2-7, find value of (a/b+b/a)+(b/c+c/b)+(c/a+a/c)
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document.write( "  \"%28a%2Fb%2Bb%2Fa%29\" + \"%28b%2Fc%2Bc%2Fb%29\" + \"%28c%2Fa%2Ba%2Fc%29\" = \"%28a%5E2+%2B+b%5E2%29%2Fab\" + \"%28b%5E2+%2B+c%5E2%29%2Fbc\" + \"%28a%5E2%2Bc%5E2%29%2Fac\" =  = \r\n" );
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document.write( "= \"%28%28a%5E2c+%2B+b%5E2c%29+%2B+%28ab%5E2+%2B+ac%5E2%29+%2B+%28a%5E2b+%2B+bc%5E2%29%29%2Fabc\" = (regroup)\r\n" );
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document.write( "=  = \r\n" );
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document.write( "=  = \r\n" );
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document.write( "   - \"3\" = \r\n" );
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document.write( "= \"%28%28a+%2B+b+%2B+c%29%2A%28ab+%2B+ac+%2B+bc%29%29%2Fabc\" - \"3\".    (1)\r\n" );
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document.write( "Now, according to the Vieta's theorem for the cubic polynomial,\r\n" );
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document.write( "a + b + c = \"-1%2F2\",         (2)  \r\n" );
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document.write( "ab+ ac + bc = \"0%2F2\" = 0,    (3)\r\n" );
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document.write( "abc = \"7%2F2\".                (4)\r\n" );
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document.write( "Substitute (2), (3) and (4) into (1) and calculate the answer:\r\n" );
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document.write( "\"a%2Fb%2Bb%2Fa\" + \"b%2Fc%2Bc%2Fb\" + \"c%2Fa%2Ba%2Fc\" = \"+%28%28-1%2F2%29%2A0%29%2F%287%2F2%29\" - 3 = -3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from this solution is \"highlight%28THIS%29\":\r
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\n" ); document.write( "\n" ); document.write( "    You do not need to solve the original equation to get the answer.\r
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\n" ); document.write( "\n" ); document.write( "    You can get the answer manipulating THE COEFFICIENTS of the original equation. \r
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\n" ); document.write( "\n" ); document.write( "To see more samples of similar solved problems, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO evaluate functions of roots of a square equation\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO evaluate functions of roots of a cubic and quartic equation\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Evaluation, substitution\".\r
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