Algebra

[Aman verma]

Q: If x = 3 + 3^2/3 + 3^ 1/3 , then the value of x^3 - 9x^2 + 18x - 12 is :

a) 1

b) 0

c) -1

d) 2^1/2

e) 3

[kvcpk]

Hi Aman,

I think the options provided are wrong.. Correct me if i am doing any mistake in my procedure..

x^3 - 9x^2 + 18x - 12 equals (x-3)^3+15
x-3 = 3^2/3 + 3^ 1/3 as per the question, which is always positive.

So the value of x^3 - 9x^2 + 18x - 12 must be greater than 15.

Are you sure about the options?

Praveen.

[Aman verma]

Hi Aman,

I think the options provided are wrong.. Correct me if i am doing any mistake in my procedure..

x^3 - 9x^2 + 18x - 12 equals (x-3)^3+15
x-3 = 3^2/3 + 3^ 1/3 as per the question, which is always positive.

So the value of x^3 - 9x^2 + 18x - 12 must be greater than 15.

Are you sure about the options?

Praveen.

Hi Praveen,

Thanks for the response ! Options are correct . The Official Answer is [spoiler]B) 0 [/spoiler]. This problem has got something to do with ( x + y + z )^3 though I don't have the solution or the Explanation , unfortunately! This is a practice assignment given in my class with only the OA provided & I'm trying to figure out the solution myself.I would really appreciate if anybody could provide a detail explanation !!

[selango]

(x-3)^3=x3-9x2+27x-27

So x3-9x2+18x-12 = (x-3)^3-9x+15

Substituting value of x we will get answer 0


I am not sure whether we will get this kind of long algebra prob in real GMAT.

[Gmat Bond]

(x-3)^3=x3-9x2+27x-27

So x3-9x2+18x-12 = (x-3)^3-9x+15

Substituting value of x we will get answer 0


I am not sure whether we will get this kind of long algebra prob in real GMAT.

You mentioned substituting value of x , but can you elaborate how we get to the answer 0.

[selango]

Well its a longer approach.But IMO these kind of prob wont appear in real GMAT.

Now coming to the prob.

We need to substitute value of x in the below statement,

(x-3)^3-9x+15

X=(3+3^1/3+3^2/3)

-->(3^1/3+3^2/3)^3-9(3+3^2/3+3^1/3)+15

Solve first term with power 3 using (a+b)^3 formula.

Now solve the equation by expanding it fully.

3^2+3^4/3+(6*3^2/3)+3^5/3+3+6*(3^1/3)-27-(9*3^2/3)-(9*3^1/3)+15

=3^2/3*(-3)+3^1/3*(-3)+3^4/3+3^5/3

=3^1/3[(-3^1/3) -3+ 3+3^4/3]

=-3^2/3+3^5/3=3^2/3[-1+1]

3^2/3*0=0




Hope this clarify

[Aman verma]

My sincere thanks to Selango ! Agreed , this type of lengthy question may not appear on the actul GMAT but it's a good practice quetion, nevertheless . An extra effort never hurts anybody !!