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Ab Surd Ity

Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).

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Binomial

By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn

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Proofs with Pictures

Some diagrammatic 'proofs' of algebraic identities and inequalities.

Particularly General

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Expand out the brackets in a systematic, organised manner.

 

You will need to use a double angle trig formula and difference of two squares. Considering $n=1$ might be useful.

 

There is perhaps no need to provide a proof for your identities if you are very clear in your mind how such a proof would be constructed, although you might wish to produce a proof if interested.