Given : a^4 + (1/a^4) = 322.
It can be written as,
⇒ a^4 + (1/a^4) = 324 - 2
⇒ a^4 + (1/a^4) + 2 = 324
⇒ (a^2 + 1/a^2)^2 = 324
⇒ (a^2 + 1/a^2) = √324
⇒ (a^2 + 1/a^2) = 18
Now,
⇒ a^2 + (1/a^2) = 16 + 2
⇒ a^2 + (1/a^2) - 2 = 16
⇒ (a - 1/a)^2 = 16
⇒ a - (1/a) = 4,-4
Hope it helps!
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Verified answer
Given : a^4 + (1/a^4) = 322.
It can be written as,
⇒ a^4 + (1/a^4) = 324 - 2
⇒ a^4 + (1/a^4) + 2 = 324
⇒ (a^2 + 1/a^2)^2 = 324
⇒ (a^2 + 1/a^2) = √324
⇒ (a^2 + 1/a^2) = 18
Now,
It can be written as,
⇒ a^2 + (1/a^2) = 16 + 2
⇒ a^2 + (1/a^2) - 2 = 16
⇒ (a - 1/a)^2 = 16
⇒ a - (1/a) = 4,-4
Hope it helps!
Verified answer