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If x = 2 + 223 + 213 then find the value of x3-6x2+6x ?

Correct Answer: 2

Explanation:

Given that  x   =   2 +   2 2 3   +   2 1 3


 


So x - 2 =  2 2 3   +   2 1 3


 


Now cubing on both sides, we get


 


 


=>  x 3 - 8 - 6 x 2 + 12 x   =   4   +   2   +   6 ( x - 2 )


 


Therefore,  x 3 - 6 x 2 + 6 x   =   - 6   +   8   =   2


 


 


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