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# If for a ≠ 0 and b ≠ 0

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If for a ≠ 0 and b ≠ 0 [#permalink]  28 Jan 2019, 01:24
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Question Stats:

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]  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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