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What are we learning ?

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.

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

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