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If x^2 + 1/x^2 = 6 then which of the following could be the value of x 22 Jan 2021, 08:30
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E
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55% (hard)

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66% (01:34) correct 34% (02:25) wrong based on 307 sessions

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If \(x^2 + \frac{1}{x^2} = 6\) then which of the following could be the value of \(x – \frac{1}{x}\)?

I. -2
II. -1
III. 2

A. I only
B. II only
C. III only
D. I and II only
E. I and III only
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E
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If x^2 + 1/x^2 = 6 then which of the following could be the value of x 22 Jan 2021, 08:46
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\((x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-2*x*\frac{1}{x}=6-2=4\)

\((x-\frac{1}{x})= +2,-2\)

ANS E
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If x^2 + 1/x^2 = 6 then which of the following could be the value of x 22 Jan 2021, 08:54
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Answer E
(x - 1/x)^2 + 2 = 6
(x - 1/x)^2 = 2^2
Then:
x - 1/x = 2 or x - 1/x = -2
Both are solvable for an x

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If x^2 + 1/x^2 = 6 then which of the following could be the value of x 26 Jan 2021, 06:01
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Bunuel
If \(x^2 + \frac{1}{x^2} = 6\) then which of the following could be the value of \(x – \frac{1}{x}\)?

I. -2
II. -1
III. 2

A. I only
B. II only
C. III only
D. I and II only
E. I and III only
Show more

Solution:

Let x - 1/x = y. Squaring both sides of this equation, we have:

x^2 + 1/x^2 - 2(x)(1/x) = y^2

Since x^2 + 1/x^2 is given to be 6 and 2(x)(1/x) = 2, we have:

6 - 2 = y^2

y^2 = 4

y = 2 or -2

Answer: E
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If x^2 + 1/x^2 = 6 then which of the following could be the value of x 01 Aug 2026, 09:38
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