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What is the value of a^4 – b^4 ?

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What is the value of a^4 – b^4 ? [#permalink]

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New post 03 Sep 2017, 06:25
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (00:41) correct 41% (00:39) wrong based on 54 sessions

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Kudos [?]: 128871 [0], given: 12183

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What is the value of a^4 – b^4 ? [#permalink]

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New post 20 Sep 2017, 11:38
Bunuel wrote:
What is the value of a^4 – b^4 ?

(1) a^2 + b^2 = 4
(2) a – b = 2


\(a^4-b^4 = (a^2+b^2)(a^2-b^2) = (a^2+b^2)(a-b)(a+b)\)

Statement 1: \((a-b)\) & \((a+b)\) cannot be calculated. Hence Insufficient

Statement 2: \((a+b)\) or \((a^2+b^2)\) cannot be calculated. Hence Insufficient

Combining 1 & 2 \((a-b)^2 = a^2+b^2-2ab\). Hence \(2ab = a^2+b^2-(a-b)^2 = 4-4=0\)
\((a+b)^2= a^2+b^2+2ab = 4+0\)
or \(a+b = 2\) or \(-2\)
So no unique solution for \((a+b)\). Hence insufficient

Option E

Last edited by niks18 on 20 Sep 2017, 12:09, edited 2 times in total.

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Re: What is the value of a^4 – b^4 ? [#permalink]

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New post 20 Sep 2017, 11:55
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Bunuel wrote:
What is the value of a^4 – b^4 ?

(1) a^2 + b^2 = 4
(2) a – b = 2

Ans C
Image

Kudos [?]: 1 [1], given: 0

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Re: What is the value of a^4 – b^4 ? [#permalink]

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New post 20 Sep 2017, 12:03
Moonlion wrote:
Bunuel wrote:
What is the value of a^4 – b^4 ?

(1) a^2 + b^2 = 4
(2) a – b = 2

Ans C
Image


Hi Moonlion

\((a+b)^2 = 4\), so \((a+b) = 2\) or \(-2\)
Thus we have two solution here and not a unique solution. Hence C cannot be the answer

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What is the value of a^4 – b^4 ? [#permalink]

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New post 24 Sep 2017, 11:08
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Answer is indeed E

Statement 1:

\(a^2+b^2=4\)
There are several values of a and b that potentially satisfy this equation.---------Insufficient

Statement 2:

\(a-b=2\)---------Insufficient

From 1 and 2; We know a=2+b
Substituting the value of a in equation below:
\(a^2+b^2=4\)
\((2+b)^2+b^2 = 4\)
.....
....
\(2b(b+2)=0\)
b=0 or b=-2

From this we can find value of a, using a-b=2
a=2 or a=0.

Hence \(a^4-b^4\) has two values. 8 and -8
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What is the value of a^4 – b^4 ?   [#permalink] 24 Sep 2017, 11:08
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