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If for a ≠ 0 and b ≠ 0
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Updated on: 30 Jan 2019, 11:48
Updated on: 30 Jan 2019, 11:48
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50% (00:41) wrong based on 4 sessions
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If a ≠ 0 and b ≠ 0, and \(a^\frac{2}{3}=b^\frac{2}{3}\) then which of the following statements must be true?
Indicate all possible values.
a) \(\frac{a}{b} =1\)
b) \(\frac{a}{b} = -1\)
c) \((\frac{a}{b})^2 =1\)
d) \(a= \frac{2}{3}\)
e) \(a^2 = b^2\)
f) \(a^\frac{1}{2} = b^\frac{1}{2}\)
Indicate all possible values.
a) \(\frac{a}{b} =1\)
b) \(\frac{a}{b} = -1\)
c) \((\frac{a}{b})^2 =1\)
d) \(a= \frac{2}{3}\)
e) \(a^2 = b^2\)
f) \(a^\frac{1}{2} = b^\frac{1}{2}\)
Show: ::
C,E
Re: If for a ≠ 0 and b ≠ 0
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28 Jan 2019, 04:37
28 Jan 2019, 04:37
1
Expert Reply
SKH121 wrote:
If a ≠ 0 and b ≠ 0, and \(a^\frac{2}{3}=b^\frac{2}{3}\) then which of the following statements must be true?
Indicate all possible values.
a) \(a/b =1\)
b) \(a/b = -1\)
c) \((a/b)^2 =1\)
d) \(a= 2/3\)
e) \(a^2 = b^2\)
f) \(a^{1/2} = b^{1/2}\)
Indicate all possible values.
a) \(a/b =1\)
b) \(a/b = -1\)
c) \((a/b)^2 =1\)
d) \(a= 2/3\)
e) \(a^2 = b^2\)
f) \(a^{1/2} = b^{1/2}\)
Show: ::
C,E
\(a^\frac{2}{3}=b^\frac{2}{3}\) =>\(\sqrt[3]{a^2}=\sqrt[3]{b^2}\).. Thus a=b or a=-b
Let us check the options
a) \(a/b =1\).....Will not be true when a=-b
b) \(a/b = -1\).....Will not be true when a=b
c) \((a/b)^2 =1\).....Will always be true for both a=b and a=-b
d) \(a= 2/3\).....Will not be true as we do not know what is a.
e) \(a^2 = b^2\).....Will always be true for both a=b and a=-b
f) \(a^{1/2} = b^{1/2}\).....Will not be true when a=-b, as for a negative term square root is undefined.
Re: If for a 0 and b 0
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03 Mar 2023, 12:32
03 Mar 2023, 12:32
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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