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
Algebra
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- kvcpk
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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.
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.
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Hi Praveen,kvcpk wrote: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.
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 !!
800. Arjun's-Bird-Eye
You mentioned substituting value of x , but can you elaborate how we get to the answer 0.selango wrote:(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.
The name is Bond, GMAT BOND !!
- selango
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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
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
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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 !!
800. Arjun's-Bird-Eye