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If \( \Large 2x^{\frac{1}{3}} + 2x^{-\frac{1}{3}} = 5 \), then \( \Large x^{\frac{1}{3}} \) is equal to

A) 1 or -1
B) 2 or \( \Large \frac{1}{2} \)
C) 8 or \( \Large \frac{1}{8} \)
D) 3 or \( \Large \frac{1}{3} \)

Correct Answer:


B) 2 or \( \Large \frac{1}{2} \)

Description for Correct answer:

Given that, \( \Large 2x^{\frac{1}{3}} + 2x^{-\frac{1}{3}} = 5 \)

Let \( \Large x^{\frac{1}{3}} = m \), then \( 2m+\frac{2}{m} = 5 \)

=> \( \Large 2m^{2} - 5m + 2 = 0 \)

=> \( \Large \left(2m - 1\right) \left(m - 2\right) = 0 \)

Therefore, \( \Large m = \frac{1}{2} \) or m = 2

=> \( \Large x^{\frac{1}{3}} = 2 \ or \ \frac{1}{2} \)

Part of solved Indices and Surd questions and answers : >> Elementary Mathematics >> Indices and Surd

Comments

Similar Questions

1). If \( \Large log3 \times log4\ x > 0 \), then

A). \( \Large x > 1 \)

B). \( \Large x > 4 \)

C). \( \Large x > 64 \)

D). none of these

2). \( \Large log \frac{1}{4} \left(a^{2}-1\right) < log_\frac{1}{2} \left(a+1\right)^{2}\)

A). \( \Large a<1 \)

B). \( \Large a<-1 \)

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A). a = b

B). a = b/2

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4). If \( \Large 2 log \left(x+1\right)-10g \left(x^{2}-1\right) = log^{2} \), then x equals

A). 1

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B). a rational number

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A). y

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A). 1

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B). HP

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9). Consider the following statements:
1. Solution of the inequality \( \Large log_{5} \left(x^{2}-11x+43\right)<2 \) is (0, 2)
2. If \( \Large [x - 1]^{ \left(log_{3}x^{2} - 2Logx^{9}\right)} = \left(x - 1\right)^{7} \), then x is 2 and 81.
Which of these is/are correct?

A). only(1)

B). only 2

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10). \( \Large log \cos x \sin x \ge 2 \) and \( \Large x \epsilon \left[ 0, 3 \pi \right] \), then \( \Large \sin x \) lines in the interval:

A). \( \Large \left[ 0, \frac{1}{2} \right] \)

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