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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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VP
Joined: 19 Oct 2018
Posts: 1080
Location: India
If x=3+3^{1/3}+3^{5/3}, then find the value of x^3-9x^2.  [#permalink]

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13 May 2019, 07:53
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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
Intern
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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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
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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