Question

I am noob help a^2+1/a^2-14
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Answer 1

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a²+1/a²-14=0

a²+1/a²=14

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Answer 2

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ALGEBRA 2 ALGEBRA QUESTION

Ahnaf A. asked • 09/16/15

If a+1/a = 4, what is the of a4+1/a4 ?

IF a + 1/a = 4 . Then what is the value of a4 + 1/a4 ?

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1 Expert Answer

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Jon P. answered • 09/16/15

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First, notice that (a + 1/a)2 = 42 = 16. But also, (a + 1/a)2 = a2 + 2a(1/a) + 1/a2 = a2 + 2 + 1/a2 = a2 + 1/a2 + 2

So a2 + 1/a2 + 2 = 16, so a2 + 1/a2 = 14.

Now, do that again...

(a2 + 1/a2)2 = 142 = 196, but also (a2 + 1/a2)2 = a4 + 2(a2)(1/a2) + 1/a4 = a4 + 2 + 1/a4 = a4 + 1/a4 + 2

So a4 + 1/a4 + 2 = 196, so a4 + 1/a4 = 194

You can see the pattern... E.g., a8 + 1/a8 = 1942 - 2, etc.

Step-by-step explanation:

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