Problem Suppose (a, b) are positive real numbers such that (a \sqrt{a}+b \sqrt{b}=183 . a \sqrt{b}+b \sqrt{a}=182). Find (\frac{9}{5}(a+b)). Hint 1 This problem will use the following elementary algebraic identity: $(x+y)^3=x^3+y^3+3 x^2 y+3 x y^2$ Can you identify what is x and what is y? Hint 2 background_video_pause_outside_viewport="on" tab_text_shadow_style="none" body_text_shadow_style="none"] Set $x=\sqrt{a}, y=\sqrt{b}$. Then the […]
In this post we have discussed AMC 10A 2018 problem number 13.
Cyclic Quadrilaterals are often important objects in a Geometry problem. Recognizing them can lead to a path to the solution. Pre RMO 2017 Problem 13 Solution is a part of our Pre-RMO problem solving series. Also visit: Math Olympiad Program of Cheenta
Tools in Geometry is very useful for pre regional mathematical olympiad, regional mathematical olympiad as well as I.S.I. & C.M.I entrance.
Cheenta is introducing open seminar for students interested in Advanced Mathematics and preparing for Pre-RMO and ISI Entrance Students. Know more..
It is interesting to represent Algebraic Identities using Geometric objects. In other words the Relationship between algebra and geometry. One easy example is presented in this video. Think! Relationship between Algebra and Geometry Also Visit: Thousand Flowers Program Try to draw the following algebraic identities using geometric objects \(a^2 - b^2 = (a+b)(a-b) \) \( (a+b)^3 = a^3 + […]
Injection Principle is an very elegant idea to count objects. This idea is useful for olympiad students as well as for the I.S.I & C.M.I. students.
This post is about the concept of Orthocenter (the intersection point of altitudes) and equal circles. Watch the videos and learn.
Learn about the Geometry of Motion in an Open Seminar organized by us. Want to Join or learn more? Get all the information here.
Bijection principle is a very useful tool for combinatorics. Here we pick up a problem that appeared in I.S.I.'s B.Stat-B.Math Entrance. Part 1: The problem and the hints Part 2 Part 3