Question

a=2+_/3 then find the value of a- 1/a​

Answer 1

Answer:

multiply it by 0 and the answer will be 9

Answer 2

Answer:

Hence, the value of a - 1/a = 0

Step-by-step explanation:

Given:-

a = 2 + √3

To find out:-

Value of a - 1/a

Solution:-

We have,

a = 2 + √3

∴ 1/a = 1/2+√3

The denomination = 2+√3

We know that

Rationalising factor of x+√y = x-√y

So, the rationalising factor of 2+√3 = 2-√3

On rationalising the denominator then

1/a = [1/(2+√3)]×[(2-√3)/2-√3)]

1/a = [1(2-√3)]/[(2+√3)(2-√3)]

1/a = (2-√3)/[(2+√3)(2-√3)]

Now, we will apply algebraic Identity in denominator because the denominator is in the form of

(x+y)(x-y) = x^2 - b^2

Where we have to put x = 2 and y = √3

1/a = (2-√3)/[(2)^2 - (√3)^2]

1/a = (2-√3)/(4 - 3)

1/a = (2-√3)/1

1/a = 2-√3

Now, we have to subtract both values a and 1/a, we get

∴ a - 1/a = 2+√3-2-√3

√3 will be cancel because they are in unlike sign , so we will cancel them.

a - 1/a = 2 - 2

a - 1/a = 0

Answer:-

Hence, the value of a - 1/a = 0

Used formulae:-

Rationalising factor of x+√y = x-√y

(x+y)(x-y) = x^2 - y^2

:)