document.write( "Question 1143178: What is the sum of the real solutions of the equation (x+1)(x^2 + 1)(x^3 + 1)=30x^3? \n" ); document.write( "

Algebra.Com's Answer #763954 by ikleyn(52805) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " The solution by @MathLover1 is fine.\r
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\n" ); document.write( "\n" ); document.write( " I came to clarify some key points of the solution and simplify it, where it is possible.\r
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document.write( "The original equation was reduced by @Mathlover1 to \r\n" );
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document.write( "     = .\r\n" );
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document.write( "I do not know simple way to factor it.\r\n" );
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document.write( "But there are online tools for it in the Internet.\r\n" );
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document.write( "See, for example, the site \r\n" );
document.write( "https://www.mathportal.org/calculators/polynomials-solvers/polynomials-expanding-calculator.php\r\n" );
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document.write( "If you apply it, you will get factorization \r\n" );
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document.write( "     = .\r\n" );
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document.write( "The factor \r\n" );
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document.write( "     =  \r\n" );
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document.write( "is always positive and, therefore, has no real roots.\r\n" );
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document.write( "So, only real roots of the quadratic polynomial   are of interest.\r\n" );
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document.write( "Since we are asked to find the sum of these roots, there is NO NEED to find the roots explicitly and individually.\r\n" );
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document.write( "By applying the Vieta's theorem, you get that their sum is equal to 3.    ANSWER\r\n" );
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