a: \(a=\sqrt{\left(20+11\sqrt{2011}\right)^2}=20+11\sqrt{2011}\)
\(b=\sqrt{\left(20-11\sqrt{2011}\right)^2}=\left|20-11\sqrt{2011}\right|=11\sqrt{2011}-20\)
P=a-b
\(=20+11\sqrt{2011}+11\sqrt{2011}-20=22\sqrt{2011}\)
b: Q=(a+1)(b+1)
\(=\left(20+11\sqrt{2011}+1\right)\left(11\sqrt{2011}-20+1\right)\)
\(=\left(21+11\sqrt{2011}\right)\left(11\sqrt{2011}-19\right)=231\sqrt{2011}-399+243331-209\sqrt{2011}\)
\(=22\sqrt{2011}+242932\)
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