Question #5c771

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Answer 1 · 2017-08-17T11:54:32

# 0.#

I hope, the Question is to determine the value of the

Expression #color(red)(x^3)-9x^2+18x-12,# given that,

#x=3+3^(1/3)+3^(2/3).#

Given that, #x=3+3^(1/3)+3^(2/3),# we have,

#x-3=3^(1/3)+3^(2/3)....(1)#

To cube both the sides, we use, #(a-b)^3=a^3-b^3-3ab(a-b).#

#:. x^3-3^3-3*3*x(x-3)#

#=(3^(1/3))^3+(3^(2/3))^3+3*3^(1/3)*3^(2/3)(3^(1/3)+3^(2/3)),#

# :. x^3-27-9x^2+27x=3+3^2+3^(1+1/3+2/3)(x-3)#.........[From (1)].

#:. x^3-9x^2+27x-27=3+9+9(x-3)=12+9x-27,#

# rArr x^3-9x^2+18x-12=0,# giving, the #"Reqd. Value="0.#

Enjoy Maths.!

Answer 2 · 2017-10-08T06:04:59

The value of the expression is #-12#.

Let us assume the expression be #color(red)(E=x^3-9x^2+18x-12)#........(1)

Now given, #x=3+3(1/3)+3(2/3)#
#:.x=3(1+1/3+2/3)#
#:.x=3xx2#
#:.x=6#.

Now, substituting the value of "#x#" in the expression (1) #rarr#

#:.E=(6)^3-9.(6)^2+18(x)-12#
#:.E=216-324+108-12#
#:.E=-12#.

Therefore, the value of the expression is #-12# (Answer).

Hope it Helps:)