# Prove is irrational.

Let k = is rational

k – 1 = (k – 1)2 = 2

k2 + 1–2k = 3 + 2 + 2 k2–2k = 5 – 1 + 2 k2–2k = 4 + 2 is rational = is rational

But, we know that is irrational.

So, our assumption is wrong.

Therefore, + + 1 is irrational.

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