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a^2 = b^2 - 1, b is not equal to 0

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Farina
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a^2 = b^2 - 1, b is not equal to 0 [#permalink] New post   04 Oct 2020, 21:48
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\(a^2\) = \(b^2- 1\), and \(b\) is not equal to \(0\)

Quantity A
Quantity B
\(a^4\)
\(b^4+1\)



A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
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B
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GreenlightTestPrep
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Re: a^2 = b^2 - 1, b is not equal to 0 [#permalink] New post   05 Oct 2020, 05:49
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Farina wrote:
\(a^2\) = \(b^2- 1\), and \(b\) is not equal to \(0\)

Quantity A
Quantity B
\(a^4\)
\(b^4+1\)



A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.


Since \(a^4 = (a^2)^2\), we can rewrite Quantity A as follows:
Quantity A: \((a^2)^2\)
Quantity B: \(b^4+1\)

Substitute:
Quantity A: \((b^2- 1)^2\)
Quantity B: \(b^4+1\)

Expand and simplify Quantity A
Quantity A: \(b^4-2b^2+1\)
Quantity B: \(b^4+1\)

Subtract \(b^4\) and subtract \(1\) from both quantities to get:
Quantity A: \(-2b^2\)
Quantity B: \(0\)

Since \(b^2\) must be positive, we can be certain that \(-2b^2\) is NEGATIVE, which means Quantity B must be greater

Answer: B
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Re: a^2 = b^2 - 1, b is not equal to 0 [#permalink] New post   06 Jan 2023, 16:12
Hello from the GRE Prep Club BumpBot!

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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Re: a^2 = b^2 - 1, b is not equal to 0 [#permalink]
06 Jan 2023, 16:12
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