MathDB

3

Part of 2017 Junior Regional Olympiad - FBH

Problems(3)

Junior Regional Olympiad - FBH 2017 Grade 7 Problem 3

Source:

9/20/2018
On blackboard there are 1010 different positive integers which sum is equal to 6262. Prove that product of those numbers is divisible with 6060
divisiblenumber theory
Junior Regional Olympiad - FBH 2017 Grade 6 Problem 3

Source:

9/20/2018
In acute triangle ABCABC holds ∠BAC=80∘\angle BAC=80^{\circ}, and altitudes hah_a and hbh_b intersect in point HH. if ∠AHB=126∘\angle AHB = 126^{\circ}, which side is the smallest, and which is the biggest in ABCABC
TriangleCompareangles
Junior Regional Olympiad - FBH 2017 Grade 8 Problem 3

Source:

9/20/2018
Find all real numbers xx such that: x−72015+x−62016+x−52017=x−20157+x−20166+x−20175 \sqrt{\frac{x-7}{2015}}+\sqrt{\frac{x-6}{2016}}+\sqrt{\frac{x-5}{2017}}=\sqrt{\frac{x-2015}{7}}+\sqrt{\frac{x-2016}{6}}+\sqrt{\frac{x-2017}{5}}
equationsquare root