A Simple Question In Disguise

Algebra

Today’s Challenge

This is a Twitter algebra challenge I found today.

It assumes basic knowledge of 1st year A Level maths content and nothing more.

Give it a try before jumping in for the solution!

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Solution

The key to this question is to make use of the Pythagorean identity

In particular, we use

Substituting this into our equation, we get

Using index laws, we have

Multiplying by the denominator/denominator in the middle term, we get

As we can see, the question is simply a quadratic in disguise

Upon factorizing, we arrive at

This means

Finally, we get

Well done!

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Happy reading,

Barry 🍩