$a^4+\frac{1}{a^4}=119$Then find $a^3+\frac{1}{a^3}$

I know $a^3+b^3=(a+b)(a^2+b^2-ab)$ and $a^4+b^4+a^2b^2=(a^2+b^2+ab)(a^2+b^2-ab)$

I try combining both but end up with equation in terms of a to the power 8, 7, 6 etc.

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- Jul 9th 2014, 04:55 AM #1

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- Jul 9th 2014, 06:53 AM #2

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## Re: a^4+1/a^4=119. Then a^3+1/a^3

Let . Then . So, and . This gives .

Then , so . Then or . Since any real number squared must be positive, it must be the first one.

So, or . This gives:

Since the square root of a positive number is positive, I put the first since and .

Hence, we have

Hence, .

- Jul 9th 2014, 07:00 AM #3

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- Jul 9th 2014, 08:43 AM #4

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- Jul 9th 2014, 09:11 AM #5

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- Jul 9th 2014, 09:32 AM #6

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- Jul 10th 2014, 04:14 AM #7

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- Jul 10th 2014, 05:56 AM #8

- Jul 10th 2014, 08:10 AM #9