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# If x and y are non-zero integers then the value of 2/(1/x^(-2)+1/y^

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Math Expert
Joined: 02 Sep 2009
Posts: 47207
If x and y are non-zero integers then the value of 2/(1/x^(-2)+1/y^  [#permalink]

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03 Sep 2017, 05:48
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72% (00:50) correct 28% (01:13) wrong based on 105 sessions

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If x and y are non-zero integers then the value of $$[\frac{2}{\frac{1}{x^{(-2)}}+\frac{1}{y^{(-2)}}}]^{(-2)}$$ can be expressed as

A. $$\frac{4}{x^4+2x^2y^2+y^4}$$

B. $$\frac{1}{x+y}$$

C. $$\frac{x^4+y^4}{4}$$

D. $$\frac{x^2+2xy+y^2}{4}$$

E. $$\frac{x^4+2x^2y^2+y^4}{4}$$

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Math Expert
Joined: 02 Aug 2009
Posts: 6292
Re: If x and y are non-zero integers then the value of 2/(1/x^(-2)+1/y^  [#permalink]

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03 Sep 2017, 08:37
Bunuel wrote:
If x and y are non-zero integers then the value of $$[\frac{2}{\frac{1}{x^{(-2)}}+\frac{1}{y^{(-2)}}}]^{(-2)}$$ can be expressed as

A. $$\frac{4}{x^4+2x^2y^2+y^4}$$

B. $$\frac{1}{x+y}$$

C. $$\frac{x^4+y^4}{4}$$

D. $$\frac{x^2+2xy+y^2}{4}$$

E. $$\frac{x^4+2x^2y^2+y^4}{4}$$

$$[\frac{2}{\frac{1}{x^{(-2)}}+\frac{1}{y^{(-2)}}}]^{(-2)}=\frac{2}{x^2+y^2}^{-2}=\frac{x^2+y^2}{2}^2=\frac{x^4+2x^2y^2+y^4}{4}$$

E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If x and y are non-zero integers then the value of 2/(1/x^(-2)+1/y^  [#permalink]

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03 Sep 2017, 08:52
Bunuel wrote:
If x and y are non-zero integers then the value of $$[\frac{2}{\frac{1}{x^{(-2)}}+\frac{1}{y^{(-2)}}}]^{(-2)}$$ can be expressed as

A. $$\frac{4}{x^4+2x^2y^2+y^4}$$

B. $$\frac{1}{x+y}$$

C. $$\frac{x^4+y^4}{4}$$

D. $$\frac{x^2+2xy+y^2}{4}$$

E. $$\frac{x^4+2x^2y^2+y^4}{4}$$

$$[\frac{2}{\frac{1}{x^{(-2)}}+\frac{1}{y^{(-2)}}}]^{(-2)}$$

$$[\frac{2}{\frac{x^{2}}{1}+\frac{y^{2}}{1}}]^{(-2)}$$

$$[\frac{2}{x^{2}+y^{2}}]^{(-2)}$$

$$[\frac{x^{2}+y^{2}}{2}]^{2}$$

$$\frac{(x^{2}+y^{2})^{2}}{4}$$

$$\frac{x^4+2x^2y^2+y^4}{4}$$

Re: If x and y are non-zero integers then the value of 2/(1/x^(-2)+1/y^ &nbs [#permalink] 03 Sep 2017, 08:52
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