If p = $\dfrac{2-\sqrt{5}}{2+\sqrt{5}}$ and q = $\dfrac{2+\sqrt{5}}{2-\sqrt{5}}$ find the values of :

(i) p + q

(ii) p - q

(iii) p² + q²

(iv) p² - q²

If x $\dfrac{\sqrt{2}-1}{\sqrt{2}+1}$ and y = $\dfrac{\sqrt{2}+1}{\sqrt{2}-1}$ , then find the value of ${x^2 +5xy + y^2}$.

Every rational number is

1. a natural number
2. an integer
3. a real number
4. a whole number

Between two rational numbers

1. there is no rational number
2. there is exactly one rational number
3. there are infinitely many rational numbers
4. there are only rational numbers and no irrational numbers.