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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

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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