Question

x^4 - 81 = 0

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation x^4 - 81 = 0, we can factor it as a difference of squares:

(x^2 - 9)(x^2 + 9) = 0

Now we can solve for x:

x^2 - 9 = 0 or x^2 + 9 = 0

Solving the first equation:

x^2 - 9 = 0
(x - 3)(x + 3) = 0

So, x = 3 or x = -3

Solving the second equation:

x^2 + 9 = 0
This equation has no real solutions since x^2 can never be negative for real numbers x.

Therefore, the solutions to the equation x^4 - 81 = 0 are x = 3 and x = -3.