If you want to be a Wrangler, you need to tackle the following (so also the problems in previous post :-)):
- If
, show that
unless
, and that if this condition is satisfied, the equations are not independent.
- Out of n straight lines whose lengths are 1, 2, 3,
inches respectively, the number of ways in which four may be chosen which will form a quadrilateral in which a circle may be inscribed is
.
- For the expansion of
, or otherwise, prove that
, where n is an integer, and the series stops at the first term that vanishes.
4. Find the real roots of the equations:
,
,
,
,
,
.
5. If the equation have a pair of equal roots, then either one of the quantities a or b is equal to one of the quantities c or d, or else
. Prove also that the roots are then
;
; or,
.
More challenges are on the way! Are you getting ready for RMO 2016? !
Nalin Pithwa