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What is the value of a^4 - b^4 ?

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Math Expert
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Joined: 02 Sep 2009
Posts: 50009
What is the value of a^4 - b^4 ?  [#permalink]

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New post 06 Feb 2018, 06:04
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

79% (00:46) correct 21% (00:29) wrong based on 31 sessions

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Joined: 07 Dec 2017
Posts: 724
Re: What is the value of a^4 - b^4 ?  [#permalink]

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New post 06 Feb 2018, 06:21
Bunuel wrote:
What is the value of a^4 - b^4 ?

(1) a^2 + b^2 = 24

(2) a^2 - b^2 = 0


As this looks like a very technical question, we'll try working with the equations.
This is a Precise approach.

(1) It isn't entirely clear how to transform a^2 + b^2 into a^4 - b^4 so simplification won't help.
Instead, we'll try numbers:
If a = 0 then b = \(\sqrt{24}\) and if b = 0 then a = \(\sqrt{24}\).
These give two different solutions, so it is insufficient!

(2) Since a^2 = b^2, then a^4 = b^4. Therefore a^4 - b^4 = 0.
Sufficient!

(B) is our answer.
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Re: What is the value of a^4 - b^4 ? &nbs [#permalink] 06 Feb 2018, 06:21
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