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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.  

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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
Suggested Book
Challenges and Thrills in Pre College Mathematics

Excursion Of Mathematics 

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