1. **Problem:** Find the positive solution of the quadratic equation $$x^2 - x - 1 = 0$$ to two significant figures. 2. **Formula:** The quadratic formula for roots of $$ax^2 + bx + c = 0$$ is: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. **Apply values:** Here, $$a=1$$, $$b=-1$$, $$c=-1$$. 4. **Calculate discriminant:** $$\Delta = b^2 - 4ac = (-1)^2 - 4 \times 1 \times (-1) = 1 + 4 = 5$$ 5. **Calculate roots:** $$x = \frac{-(-1) \pm \sqrt{5}}{2 \times 1} = \frac{1 \pm \sqrt{5}}{2}$$ 6. **Evaluate positive root:** $$x = \frac{1 + \sqrt{5}}{2} \approx \frac{1 + 2.236}{2} = \frac{3.236}{2} = 1.618$$ 7. **Round to two significant figures:** $$x \approx 1.6$$ **Final answer:** (a) 1.6