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document.write( " This equation of the degree 4 is VERY SPECIAL.\r
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document.write( " It relates to the class of so named palindromic equations of the degree 4, which means that its coefficients \r
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document.write( " form a palindromic sequence.\r
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document.write( " See this Wikipedia article https://en.wikipedia.org/wiki/Reciprocal_polynomial#Palindromic_polynomial\r
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document.write( " There is a SPECIAL PROCEDURE in algebra to solve such equations. It is presented below.\r
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document.write( "
= 0 (1)\r\n" );
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document.write( "It follows from the equation that x= 0 IS NOT the root.\r\n" );
document.write( "So, we can divide both sides by 
without loosing the roots. In this way, you will get an equivalent equation\r\n" );
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= 0.\r\n" );
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document.write( "Group and re-write it equivalently in the form\r\n" );
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document.write( "
- 
+ 50 = 0, or\r\n" );
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+ 50 = 0. (2)\r\n" );
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document.write( "Introduce new variable u = 
+ 
. Then equation (2) takes a form\r\n" );
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= 0.\r\n" );
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document.write( "Solve this quadratic equation using the quadratic formula\r\n" );
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= 
= 
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document.write( "The two roots are \r\n" );
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= 
= 
= 
= 
and\r\n" );
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= 
= 
= 
= 
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document.write( "Now, to find x, we need to solve two equations\r\n" );
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document.write( " a) + = and b) + = .\r\n" );
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document.write( "Case a). + = \r\n" );
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= 0\r\n" );
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= 
= 
= 
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document.write( " So, the two roots are 
= 
= 3 and 
= 
= 
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document.write( "Case b). + = \r\n" );
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= 0\r\n" );
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= 
= 
= 
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document.write( " So, the two roots are 
= 
= 2 and 
= 
= 
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document.write( "ANSWER. The four roots are , , 2 and 3.\r\n" );
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document.write( "Solved.\r
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document.write( "The lesson to learn\r
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document.write( " From this post learn on how to solve palindromic equations.\r\n" );
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document.write( " Every palindromic equation of the degree 4 can be solved in this way.\r\n" );
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document.write( "The major steps of the solution are :\r
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document.write( " a) Divide both sides by ;\r\n" );
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document.write( " b) Introduce new variable u = x + ;\r\n" );
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document.write( " c) Reduce the equation to a quadratic equation relative new variable u and solve it getting two roots and ;\r\n" );
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document.write( " d) Then find x by solving two equations 
= and = .\r\n" );
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document.write( "Again :\r
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document.write( " Every palindromic equation of the degree 4 can be solved in this way.\r\n" );
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