INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

December 30, 2019

An interesting biquadratic from ISI Entrance 2005

Problem

Let $a,b$ and $c$ be the sides of a right angled triangle. Let $ \displaystyle{\theta } $ be the smallest angle of this triangle. If $ \displaystyle{ \frac{1}{a}, \frac{1}{b} } $ and $ \displaystyle{ \frac{1}{c} }$ are also the sides of a right angled triangle then show that $ \displaystyle{ \sin\theta=\frac{\sqrt{5}-1}{2}}$

Topic

Biquadratic Equations

Main Idea

It is usually hard to solve biquadratic equations. However, sometimes, combining tools from geometry and strategies like completing the square it is possible to do so.

Source

I.S.I. B.Stat. Entrance 2005, Subject Problem 1

Suggested Book

Challenges and Thrills in Pre College Mathematics
Excursion Of Mathematics

Watch video

Knowledge graph.

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com
enter