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If ab ≠ 0, is a^4 + 1/a^2 + a^{−2} = 1 + b^{−2}/b^{−2} + b^{−4}? 1) a

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If ab ≠ 0, is a^4 + 1/a^2 + a^{−2} = 1 + b^{−2}/b^{−2} + b^{−4}? 1) a [#permalink] New post   18 Apr 2021, 01:34
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If \(ab ≠ 0\), is \(\frac{a^4 + 1}{a^2 + a^{−2}}=\frac{1 + b^{−2}}{b^{−2} + b^{−4}}\)?

(1) \(ab = 1\)

(2) \(\frac{a}{b} = 1\)
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Re: If ab ≠ 0, is a^4 + 1/a^2 + a^{−2} = 1 + b^{−2}/b^{−2} + b^{−4}? 1) a [#permalink] New post   18 Apr 2021, 01:53
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If \(ab ≠ 0\), is \(\frac{a^4 + 1}{a^2 + a^{−2}}=\frac{1 + b^{−2}}{b^{−2} + b^{−4}}\)?

Is \(\frac{a^4 + 1}{a^2 + a^{−2}}=\frac{1 + b^{−2}}{b^{−2} + b^{−4}}\)?

Is \(\frac{a^4 + 1}{a^2 + \frac{1}{a^2}}=\frac{1 + \frac{1}{b^2}}{\frac{1}{b^2} + \frac{1}{b^4}}\)?

Is \(\frac{a^4 + 1}{\frac{a^4 + 1}{a^2}}=\frac{\frac{b^2+1}{b^2}}{\frac{b^2+1}{b^4}}\)?

Is \((a^4 + 1)*\frac{a^2}{a^4 + 1}=\frac{b^2+1}{b^2}*\frac{b^4}{b^2+1}\)?

Is \(a^2= b^2\)?


(1) \(ab = 1\). Not sufficient.


(2) \(\frac{a}{b} = 1\) --> \(a = b\) --> \(a^2 = b^2\). Sufficient.


Answer: B.
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Re: If ab ≠ 0, is a^4 + 1/a^2 + a^{−2} = 1 + b^{−2}/b^{−2} + b^{−4}? 1) a [#permalink] New post   18 Apr 2021, 02:34
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Asked: If \(ab ≠ 0\), is \(\frac{a^4 + 1}{a^2 + a^{−2}}=\frac{1 + b^{−2}}{b^{−2} + b^{−4}}\)?

\(\frac{a^4 + 1}{a^2 + a^{−2}} = \frac{a^6+ a^2 }{a^4 + 1} = a^2\)
\( \frac{1 + b^{−2}}{b^{−2} + b^{−4}}= \frac{b^4 + b^2}{b^2 + 1}= b^2\)

Q. is a^2 = b^2?

(1) \(ab = 1\)
a = 1/b
a^2 = 1/b^2
If b=1; TRUE
But if b<>1; FALSE
NOT SUFFICIENT

(2) \(\frac{a}{b} = 1\)[/quote]
a = b
a^2 = b^2
SUFFICIENT

IMO B
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Re: If ab ≠ 0, is a^4 + 1/a^2 + a^{−2} = 1 + b^{−2}/b^{−2} + b^{−4}? 1) a [#permalink]
18 Apr 2021, 02:34
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