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Need assistance with solving sextic (degree 6 polynomial) equation

Posted by White Group Mathematics on February 7, 2015 at 3:30 AM


Find all real numbers of x which satisfy the equation


(1+x)^6-2(1-x)^6=(1-x^2)^3


Please help.


Student X









(1+x)^6-2(1-x)^6=(1-x^2)^3



 

(1+x)^6-2(1-x)^6=(1-x)^3 * (1+x)^3 -----------(1)



 

Let a=(1+x)^3, b=(1-x)^3, then (1) becomes   a^2 -2b^2 = ab


Migrating all terms to the LHS,



 

a^2 -ab -2b^2 =0



 

(a-2b)(a+b) =0



 

a=2b or a=b



 

Resubstitute the expressions for both a and b in terms of x, you should arrive at the required answers shortly.



 

Peace.





 

Best Regards,

 

 

Mr Koh



Categories: Math Queries

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