(i) If x = $\dfrac{7 + 3\sqrt{5}}{7- 3\sqrt{5}}$ , find the value of $x^2 + \dfrac{1}{x^2}$

(ii) If x = $\dfrac{\sqrt{5} - \sqrt{2}}{\sqrt{5} + \sqrt{2}}$ and y = $\dfrac{\sqrt{5} + \sqrt{2}}{\sqrt{5} - \sqrt{2}}$ , find the value of x² + xy + y²

(iii) If x = $\dfrac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}$ and y = $\dfrac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}$ , find the value of x³ + y³.

Write the following real numbers in descending order :

$\sqrt{2}, 3.5, \sqrt{10}, -\dfrac{5}{\sqrt{2}}, {\dfrac{5}{2}}{\sqrt{3}}$

Insert three irrational numbers between $2\sqrt{3}$ and $2\sqrt{5}$ , and arrange in descending order.

Give an example each of two different irrational numbers , whose

(i) sum is an irrational number.

(ii) product is an irrational number.