Math, asked by shabnamparveen000000, 8 months ago

If a = 2 +√3, then find the value of a—1/a​

Answers

Answered by badboy4089
1

Step-by-step explanation:

Heya friend,

Here is the answer you were looking for:

\begin{lgathered}a = 2 + \sqrt{3} \\ \\ \frac{1}{a} = \frac{1}{2 + \sqrt{3} } \\\end{lgathered}

a=2+

3

a

1

=

2+

3

1

On rationalizing the denominator we get,

\begin{lgathered}\frac{1}{a} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\\end{lgathered}

a

1

=

2+

3

1

×

2−

3

2−

3

Using the identity :

(x + y)(x - y) = {x}^{2} - {y}^{2}(x+y)(x−y)=x

2

−y

2

\begin{lgathered}\frac{1}{a} = \frac{2 - \sqrt{3} }{ {(2)}^{2} - {( \sqrt{3} )}^{2} } \\ \\ \frac{1}{a} = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \frac{1}{a} = 2 - \sqrt{3} \\ \\ a - \frac{1}{a}\end{lgathered}

a

1

=

(2)

2

−(

3

)

2

2−

3

a

1

=

4−3

2−

3

a

1

=2−

3

a−

a

1

Putting the values,

\begin{lgathered}a - \frac{1}{a} = (2 + \sqrt{3} ) - (2 - \sqrt{3} ) \\ \\ a - \frac{1}{a} = 2 + \sqrt{3} - 2 + \sqrt{3} \\ \\ a - \frac{1}{a} = \sqrt{3} + \sqrt{3} \\ \\ a - \frac{1}{a} = 2 \sqrt{3}\end{lgathered}

a−

a

1

=(2+

3

)−(2−

3

)

a−

a

1

=2+

3

−2+

3

a−

a

1

=

3

+

3

a−

a

1

=2

3

Answered by sona972
0

Step-by-step explanation:

2+✓3-1/2+✓3

(2+✓3)²-1/2+✓3

4+4✓3+3/2+✓3

7+4✓3/2+✓3

(7+4✓3)(2-✓3)/(2+✓3)(2-✓3)

14-7✓3+8✓3-12/4-3

2+✓3/1

ans is 2+✓3

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