Question

If a=√(2)+1, then find the value of a - 1 /a​

Answer 1

Answer:

a - 1 /a​

$(\sqrt{2}+1) - \frac{1}{(\sqrt{2}+1)} \\\frac{(\sqrt{2}+1) (\sqrt{2}+1) }{(\sqrt{2}+1)} - \frac{1}{(\sqrt{2}+1)}\\\frac{\sqrt{2}(\sqrt{2}+1)+ 1(\sqrt{2}+1) }{(\sqrt{2}+1)} - \frac{1}{(\sqrt{2}+1)}\\\frac{(2+\sqrt{2}+\sqrt{2}+1) -1 }{(\sqrt{2}+1)} \\\frac{(3+2\sqrt{2}) -1 }{(\sqrt{2}+1)} \\\frac{3+2\sqrt{2} -1 }{(\sqrt{2}+1)}\\\frac{2+2\sqrt{2} }{\sqrt{2}+1}$

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