Final answer:
To solve for x in the equation (x²-1)¹ - 1, you simplify it to x² - 2 = 0 and then find that the solutions for x are ±√2.
Step-by-step explanation:
To solve for x in the equation (x²-1)¹ - 1, we should first simplify the equation. Noticing that raising anything to the power of 1 keeps it unchanged, the expression simplifies to x² - 1 - 1. This further reduces to x² - 2 = 0. Now, we can solve for x using basic algebra:
- Add 2 to both sides: x² = 2.
- Take the square root of both sides: x = ±√2.
Thus, the solutions for x are ±√2.