Here are the questions asked in Regional Math Olympiad 2017 and their solutions. Try to solve it first and then see the solutions.
Looking for just the problems? Download the PDF here.
RMO 2017, Problem 1:
Let AOB be a given angle less than \( 180^o \) and let P be an interior point of the angular region determined by \( \angle AOB \) . Show, with proof, how to construct, using only ruler and compass, a line segment CD passing through P such that C lies on the ray OA and D lies on the ray OB and CP:PD = 1:2.
RMO 2017, Problem 2:
Show that the equation $$ a^3 + (a+1)^3 + (a+2)^3 + (a+3)^3 + (a+4)^3 + (a+5)^3 + (a+6)^3 = b^4 + (b+1)^4 $$ has no solutions in integer a, b.
RMO 2017, Problem 3:
Let
RMO 2017, Problem 4:
Consider
RMO 2017, Problem 5:
Let
RMO 2017, Problem 6:
Let x, y, z be real numbers, each greater than 1. Prove that
$\frac{x+1}{y+1}$ + $\frac{y+1}{z+1}$ + $\frac{z+1}{x+1}$ $\leq$ $\frac{x-1}{y-1}$ + $\frac{y-1}{z-1}$ + $\frac{z-1}{x-1}$.
~ Discussion by Souvik Mondal & Writabrata Bhattacharya (Associate Faculty - Cheenta)
Here are the questions asked in Regional Math Olympiad 2017 and their solutions. Try to solve it first and then see the solutions.
Looking for just the problems? Download the PDF here.
RMO 2017, Problem 1:
Let AOB be a given angle less than \( 180^o \) and let P be an interior point of the angular region determined by \( \angle AOB \) . Show, with proof, how to construct, using only ruler and compass, a line segment CD passing through P such that C lies on the ray OA and D lies on the ray OB and CP:PD = 1:2.
RMO 2017, Problem 2:
Show that the equation $$ a^3 + (a+1)^3 + (a+2)^3 + (a+3)^3 + (a+4)^3 + (a+5)^3 + (a+6)^3 = b^4 + (b+1)^4 $$ has no solutions in integer a, b.
RMO 2017, Problem 3:
Let
RMO 2017, Problem 4:
Consider
RMO 2017, Problem 5:
Let
RMO 2017, Problem 6:
Let x, y, z be real numbers, each greater than 1. Prove that
$\frac{x+1}{y+1}$ + $\frac{y+1}{z+1}$ + $\frac{z+1}{x+1}$ $\leq$ $\frac{x-1}{y-1}$ + $\frac{y-1}{z-1}$ + $\frac{z-1}{x-1}$.
~ Discussion by Souvik Mondal & Writabrata Bhattacharya (Associate Faculty - Cheenta)