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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
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What is the value of a^4 - b^4? 1) a^2 - b^2 = 16 2) a + b = [#permalink] New post 25 Nov 2007, 15:06
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What is the value of a^4 - b^4?

1) a^2 - b^2 = 16
2) a + b = 8
VP
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Re: DS: Exponents! [#permalink] New post 25 Nov 2007, 16:38
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
Director
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 [#permalink] New post 25 Nov 2007, 16:46
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.
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 [#permalink] New post 25 Nov 2007, 22:35
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 :)
  [#permalink] 25 Nov 2007, 22:35
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