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x= 1/2-

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x= 1/2-

by Max@Math Revolution » Thu Apr 30, 2020 6:21 am

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[GMAT math practice question]

\(X=\frac{1}{2-\sqrt[3]{2}}\) . What is the value of 3x^3-6x^2+3x?

A. 1/2
B. 1
C. 3/2
D. 2
E. 5/2
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Re: x= 1/2-

by Max@Math Revolution » Sun May 03, 2020 7:31 pm
=>

\(X=\frac{1}{2-\sqrt[3]{2}}\)

⇔ x(2- \(\sqrt[3]{2}\) )=1
⇔ 2x- \(\sqrt[3]{2}\) x=1
⇔ 2x-1= \(\sqrt[3]{2}\) x
⇔ (2x-1)^3=( \(\sqrt[3]{2}\) x)^3
⇔ 8x^3-12x^2+6x-1=2x^3
⇔ 6x^3-12x^2+6x-1=0
⇔ 6x^3-12x^2+6x=1
⇔ 3x^3-6x^2+3x=1/2

Therefore, A is the answer.
Answer: A
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