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# What is the value of a^4 - b^4? 1) a^2 - b^2 = 16 2) a + b =

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Director
Joined: 01 May 2007
Posts: 793

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What is the value of a^4 - b^4? 1) a^2 - b^2 = 16 2) a + b = [#permalink]

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25 Nov 2007, 16:06
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What is the value of a^4 - b^4?

1) a^2 - b^2 = 16
2) a + b = 8

Kudos [?]: 385 [0], given: 0

VP
Joined: 09 Jul 2007
Posts: 1098

Kudos [?]: 144 [0], given: 0

Location: London

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25 Nov 2007, 17:38
jimmyjamesdonkey wrote:
What is the value of a^4 - b^4?

1) a^2 - b^2 = 16
2) a + b = 8

1. a^2-b^2=16
a^2=16+b^2 not suff.

2. a=8-b
a^2=64-16b+b^2 not suff.

combined

16+b^2=64-16b+b^2

16b=48
b=3

a=5

C

any other inputs

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Director
Joined: 01 May 2007
Posts: 793

Kudos [?]: 385 [0], given: 0

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25 Nov 2007, 17:46
Can you explain why I can't just take statement #1 and square each term:

a^2-b^2=16

(a^2)^2 - (b^2)^2 = 16^2?

I thought that would give me: a^4 - b^4 = 16^4

You are correct with C.

Kudos [?]: 385 [0], given: 0

SVP
Joined: 01 May 2006
Posts: 1794

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25 Nov 2007, 23:35
jimmyjamesdonkey wrote:
Can you explain why I can't just take statement #1 and square each term:

a^2-b^2=16

(a^2)^2 - (b^2)^2 = 16^2?

I thought that would give me: a^4 - b^4 = 16^4

You are correct with C.

We cannot do so .... It is missing a term and the sign is wrong.

x-y = 2
=> (x-y)^2 = 2^2
<=> x^2 - 2*x*y + y^2 = 4

... the power of 2 is not distributive as a multiplication is

Kudos [?]: 169 [0], given: 0

25 Nov 2007, 23:35
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