If a = √2 +1, then find the value of \(a - \frac{1}{a}\).

1.	If a = √2 +1, then find the value of \(a - \frac{1}{a}\).
Answer» Given: a = √2 + 1 \(\frac{1}{a} = \frac{1}{(\sqrt2+1)}\) \(= \frac{1}{(\sqrt2+1)}\) x \(\frac{(\sqrt2-1)}{(\sqrt2-1)}\) \(= \frac{(\sqrt2-1)}{((\sqrt2)^2 - (1)^2)}\) \(= \frac{(\sqrt2-1)}{1}\) \(= \sqrt2-1\) Now, \(a - \frac{1}{a}\) = (√2 + 1) – (√2 – 1) = √2 + 1 - √2 + 1 = 2

Answer»

Given: a = √2 + 1

\(\frac{1}{a} = \frac{1}{(\sqrt2+1)}\)

\(= \frac{1}{(\sqrt2+1)}\) x \(\frac{(\sqrt2-1)}{(\sqrt2-1)}\)

\(= \frac{(\sqrt2-1)}{((\sqrt2)^2 - (1)^2)}\)

\(= \frac{(\sqrt2-1)}{1}\)

\(= \sqrt2-1\)

Now,

\(a - \frac{1}{a}\) = (√2 + 1) – (√2 – 1)

= √2 + 1 - √2 + 1

= 2

Discussion

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