Question

if a= √2 -1 then find a +1/a ​

Answer 1

Given :-

★ a = √2 -1

To Find :-

The value of a +1/a

Concept :-

★ At first, we have to find 1/a

★ After that we have to rationalise the denominator.

Solution :-

Given that,

a = √2 -1

Therefore,

⟹ 1/a = 1/(√2-1)

⟹ 1/a = (√2+1)/( √2 -1) (√2+1)

⟹ 1/a = (√2+1)/(2-1)

⟹ 1/a = √2 +1

Formula used :-

a² - b² =(a+b) (a-b)

Now,

a +1/a

= √2 +1 + √2 -1

= 2√2

Hence,

the required answer is = 2√2

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