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find the value of
(a-(1)/(a) )^2 and
(a-(1)/(a) ), when
a^(2) +(1)/(a^2)=18

User OShiffer
by
7.6k points

1 Answer

1 vote

Answer:

To find the value of (a - 1/a)^2 and (a - 1/a), we can start by squaring the given equation:

a^2 + 1/a^2 = 18

(a^2 + 1/a^2)^2 = 18^2

a^4 + 2 + 1/a^4 = 324

a^4 + 1/a^4 = 322

Now, to find (a - 1/a)^2, we can square the difference of a and 1/a:

(a - 1/a)^2 = a^2 - 2 + 1/a^2

We can substitute the value of a^4 + 1/a^4 = 322 into this equation:

(a - 1/a)^2 = 322 - 2

(a - 1/a)^2 = 320

To find (a - 1/a), we can take the square root of (a - 1/a)^2:

(a - 1/a) = √320

And, a^2 + 1/a^2 = 18, we can solve for a,

a^4 - 18a^2 + 1 = 0

(a^2 - 1)(a^2 - 18) = 0

a^2 = 1 or a^2 = 18

a = 1 or a = ±√18

So, in this case, the value of (a - 1/a)^2 is 320 and (a - 1/a) is √320.

Explanation:

User Jeff Shaver
by
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