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If x=3+3^{1/3}+3^{5/3}, then find the value of x^3-9x^2.

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Joined: 19 Oct 2018
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If x=3+3^{1/3}+3^{5/3}, then find the value of x^3-9x^2.  [#permalink]

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New post 13 May 2019, 07:53
1
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A
B
C
D
E

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(N/A)

Question Stats:

25% (01:08) correct 75% (02:51) wrong based on 8 sessions

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If x=\(3+3^{1/3}+3^{5/3}\), then find the value of \(x^3-9x^2\) .

A. 81
B. 111
C. 150
D. 186
E. 192
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Joined: 07 May 2019
Posts: 11
If x=3+3^{1/3}+3^{5/3}, then find the value of x^3-9x^2.  [#permalink]

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New post 13 May 2019, 09:10
nick1816 wrote:
If x=\(3+3^{1/3}+3^{5/3}\), then find the value of \(x^3-9x^2\) .

A. 81
B. 111
C. 150
D. 186
E. 192


    \(x=3+3^{1/3}+3^{5/3}\)
Taking 3 to the other side
    \(x – 3 = 3^{1/3} +3^{5/3}\)
Cubing both sides we get:
    \(x^3 – 27 – 3*3*x(x-3) = 3 + 3^5 + 3.3^{1/3}.3^{5/3}(3^{1/3} + 3^{5/3})\)
    \(x^3 – 27 – 9x^2 + 27x = 246 + 27 (x- 3)\) {Replaced \(3^{1/3} + 3^{5/3}\)with \((x-3)\)}
    \(x^3 – 27 – 9x^2 + 27x = 246 + 27x – 81\)
    \(x^3 – 9x^2 = 27 + 246 – 81 = 192\)

Hence the correct answer is Option E
GMAT Club Bot
If x=3+3^{1/3}+3^{5/3}, then find the value of x^3-9x^2.   [#permalink] 13 May 2019, 09:10
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If x=3+3^{1/3}+3^{5/3}, then find the value of x^3-9x^2.

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