Q6 of 128 Page 18

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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