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# What is the value of a^4 – b^4 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 49496
What is the value of a^4 – b^4 ?  [#permalink]

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03 Sep 2017, 06:25
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Difficulty:

25% (medium)

Question Stats:

76% (01:27) correct 24% (01:29) wrong based on 103 sessions

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What is the value of a^4 – b^4 ?

(1) a^2 + b^2 = 4
(2) a – b = 2

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Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
What is the value of a^4 – b^4 ?  [#permalink]

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Updated on: 20 Sep 2017, 12:09
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

Originally posted by niks18 on 20 Sep 2017, 11:38.
Last edited by niks18 on 20 Sep 2017, 12:09, edited 2 times in total.
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Joined: 07 Jan 2016
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Re: What is the value of a^4 – b^4 ?  [#permalink]

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20 Sep 2017, 11:55
1
Bunuel wrote:
What is the value of a^4 – b^4 ?

(1) a^2 + b^2 = 4
(2) a – b = 2

Ans C
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Joined: 25 Feb 2013
Posts: 1217
Location: India
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Re: What is the value of a^4 – b^4 ?  [#permalink]

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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

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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24 Sep 2017, 11:08
1

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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