document.write( "Question 76096: This problem is from my daughter's (Arundhati's) VIII standard text book on advanced mathematics. I checked it through a calculator, the expressions comes to 4, but how to solve it: \r
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Algebra.Com's Answer #54636 by Edwin McCravy(20077) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "This problem is from my daughter's (Arundhati's) VIII \r\n" );
document.write( "standard text book on advanced mathematics. I checked \r\n" );
document.write( "it through a calculator, the expressions comes to 4, \r\n" );
document.write( "but how to solve it: \r\n" );
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document.write( "Prove that \r\n" );
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document.write( "It is well known that a solution to the cubic equation\r\n" );
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document.write( " is given by the formula\r\n" );
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document.write( "Since your expression is of this form, let's find the \r\n" );
document.write( "values of p and q that would make this equivalent to \r\n" );
document.write( "your expression. To do this we equate like parts\r\n" );
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document.write( "The first gives q = -40\r\n" );
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document.write( "Substituting that in the second equation:\r\n" );
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document.write( "Squaring both sides:\r\n" );
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document.write( "Multiply both sides by 27\r\n" );
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document.write( "Taking cube roots of both sides:\r\n" );
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document.write( "So your expression is a solution to the cubic\r\n" );
document.write( "equation   or\r\n" );
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document.write( "By DesCartes rule of signs, this cubic has\r\n" );
document.write( "just one positive solution, so your expression\r\n" );
document.write( "must be it.\r\n" );
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document.write( "Direct substitution of 4 into this equation shows\r\n" );
document.write( "that 4 is its only positive solution:\r\n" );
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document.write( "Since the cubic equation  can have but \r\n" );
document.write( "one positive solution, and both your expression and 4 \r\n" );
document.write( "must be this positive solution, your expression must\r\n" );
document.write( "equal 4.\r\n" );
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document.write( "Edwin

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