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Why does $1-\sqrt{1-4pq} = 1-|p-q |$ for $p \in (0,1)$ and $q=1-p$ ?

How can I factor $1-\sqrt{1-4pq}$ to prove the above identity ?

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1 Answer 1

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Hint:

Subsitute $q=1-p$ into both sides. Notice then the equality you need to prove, and it will be immediate to you why it is true.

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