document.write( "Question 1075766: Let $f(x) = x^3+bx+c$, where $b$ and $c$ are integers.\r
\n" ); document.write( "\n" ); document.write( "If $f(5+\sqrt 3)=0$, determine $b+c$. \n" ); document.write( "

Algebra.Com's Answer #690449 by ikleyn(53937) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "If you really came from \"Art of problem solving\" (as the tutor KMST think), it should be an elementary assignment for you.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You are given that \r\n" );
document.write( "\r\n" );
document.write( " = 0    (if I correctly read your formula).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Expand the parentheses. You will get a long expression in the left side of the equation, in which some terms go \r\n" );
document.write( "with the multiplier , while the other terms go without this multiplier.\r\n" );
document.write( "\r\n" );
document.write( "Combine the terms in the left side in two groups. One group contains all the terms with the multiplier ,\r\n" );
document.write( "while the other group does not contain such terms.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then your original equation will deploy in TWO equations for each of the two groups separately.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus you will get TWO equations for the unknowns \"b\" and \"c\".\r\n" );
document.write( "You will be able easily solve these equations and find \"b\" and \"c\" separately. \r\n" );
document.write( "\r\n" );
document.write( "Then calculate \"b+c\".\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "For the person who got this assignment, these explanations (these hints) are more than enough.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " H a p p y l e a r n i n g !\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " C o m e a g a i n ! !\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );