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? !