Question

If a=2+√3, then find value of a+1/a

Answer 1

Step-by-step explanation:

Given,

a = 2 + √3

1/a = 1/(2 + √3)

now rationalise the denominator,

you can rationalise by multiplying the numerator and denominator both by the conjugate of denominator.

If a number is, √3 + √2, then it's conjugate is √3 - √2

In the same way,

conjugate of 2+√3 is 2 - √3.

So,

1/a = 1/(2+√3)

= (1/2+√3) × (2 - √3/ 2 + √3)

= 2 - √3 / 2² - (√3)²

= 2 - √3 / 4 - 3

= 2 - √3 / 1

= 2 - √3

So, 1/a = 2 - √3

a + 1/a

= 2 + √3 + 2 - √3

= 4

Note, if you want to learn more about rationalising a number, refer to the chapter Rational Number (class 9) in your maths book or just ask your teacher.

Hope it helps!

Mark me brainliest!

Answer 2

Answer:

4

Step-by-step explanation:

As we have given in the question i.e. a$=2+\sqrt{3}$ and we need to find the value of $a+\dfrac{1}{a}$

To solve it first we would do rationalization of 1/a

As $\dfrac{1}{a}=\dfrac{1}{2+\sqrt{3} }$ we would multiply both numerator and denominator by the conjugate of denominator i.e.

$2-\sqrt{3}$

After rationalization we have $\dfrac{1}{a}=\dfrac{2-\sqrt{3} }{4-3}$

$=\dfrac{2-\sqrt{3} }{1}$

So we need to find a+1/a i.e.$2+\sqrt{3} +2-\sqrt{3}=4$

Therefore our final answer would be 4