Question #5c771

2 Answers

0.

Explanation:

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.!

Oct 8, 2017

The value of the expression is -12.

Explanation:

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:)