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If for a ≠ 0 and b ≠ 0

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If for a ≠ 0 and b ≠ 0 [#permalink] New post 28 Jan 2019, 01:24
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100% (01:37) correct 0% (00:00) wrong based on 1 sessions
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) \(a^\frac{1}{2} = b^\frac{1}{2}\)

[Reveal] Spoiler:
C,E

Last edited by Carcass on 30 Jan 2019, 11:48, edited 2 times in total.
formatted the Q
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Re: If for a ≠ 0 and b ≠ 0 [#permalink] New post 28 Jan 2019, 04:37
Expert's post
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) \(a^{1/2} = b^{1/2}\)

[Reveal] Spoiler:
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.
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: If for a ≠ 0 and b ≠ 0   [#permalink] 28 Jan 2019, 04:37
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