An interesting biquadratic from ISI Entrance 2005

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What are we learning ?

Competency in Focus: 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.  

Look at the knowledge graph.

Next understand the 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}}

Source of the problem

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

Key Competency
Biquadratic Equation
Difficulty Level
6/10
Suggested Book
Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics 

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