Question

if a =2+✓3 then what will be a×1/a​

Answer 1

Q. If a=2+ 3, then find the value of a a− a1

ANSWER:-

Given that,

a=2+ 3

Then, Value of

a− a1 =2+ 3 − 2+ 3

1 =2+ 3− 2+ 3

1× 2− 3

2− 3onrationalize

=2+ 3

− 4−3(2− 3 )

=2+ 3 −2+ 3

=2 3

Hence, this is the answer.

Answer 2

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Here is Answer you Were Looking For:-

a = 2 + √3

1/a = 1/2+√3

On Rationalizing the Denominator

We get,

1/a = 1/2+√3 × 2-√3/2-√3

Using the Identity:-

(x+y)(x-y) = x² - y²

1/a = 2-√3/(2)²-(√3)²

1/a = 2-√3/4-3

1/a = 2-√3

a - 1/a

Putting the Values,

a - 1/a = (2+√3)-(2-√3)

a - 1/a = 2+√3-2+√3

a - 1/a = √3 + √3

a - 1/a = 2√3.