Exercises:

- Show that is symmetric with respect to a, b, c, d.
- Show that the following expressions are cyclic with respect to a, b, c, d, taken in this order: and
- Expand the expression using notation:
- Expand the expression using notation:
- Prove that
- Prove that
- Prove that
- Prove that :
- Prove that:
- Prove that : .
- Prove that:
- Prove that:
- Prove that:
- Prove that:
- If one of the numbers a, b, and c is the geometric mean of the other two, use the previous problem to prove the following:
- If the numbers x, y, z taken in some order or other form an AP, use problem 3 to prove that
- Express as the sum of three squares. Hence, show that is negative for all real values of a, b, c except when . Hint: Put , , , and notice that .
- If , show that (i) ; (ii) (iii) can be expressed in the form ; and, find p, q, r in terms of a, b, c, f, g, h.

Cheers,

Nalin Pithwa.

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