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: