How do you solve #x^2 - x - 1 = 0#?
Use the quadratic formula or complete the square to find:
#x = (1+-sqrt(5))/2#
Method 1 - Quadratic Formula
This has solutions given by the quadratic formula
Method 2 - Completing the square
So:
How are the two methods related?
Hence:
So:
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You can solve the equation (x^2 - x - 1 = 0) using the quadratic formula, which is (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}), where (a = 1), (b = -1), and (c = -1). Plugging in these values gives you (x = \frac{1 \pm \sqrt{1 - 4(-1)(-1)}}{2}). Simplifying further yields (x = \frac{1 \pm \sqrt{1 - 4}}{2}), which becomes (x = \frac{1 \pm \sqrt{5}}{2}). Therefore, the solutions are (x = \frac{1 + \sqrt{5}}{2}) and (x = \frac{1 - \sqrt{5}}{2}).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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